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1.34k
IPhOElectroMagnetic
math_p_numeric
[ { "content": "A charged particle with charge 1.7 C and mass 1.09 kg is initially launched from origin in the space. It has an initial velocity of 0.64 m/s in the x-direction and 1.69 m/s in the y-direction. There is a uniform electric field of strength 1.11 along the XY plane, making an angle of 324.6 degrees w...
math
{ "ground_truth": "3.5735584084630133e-13", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 343, "json_index": null, "split": "test" }
343
IPhOPulley
math_p_numeric
[ { "content": "In a system called 'massprismpulleyplane_0', a large movable prism of mass 12.35 kg rests on a plane inclined at 0.0 degrees. The prism is inclined at an angle of 15.11 degrees on the left side and 35.21 degrees on the right side. Two blocks of mass 1.96 kg and 4.17 kg are resting on the left and ...
math
{ "ground_truth": "6.041636629167905", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 344, "json_index": null, "split": "test" }
344
BasicInclinedPlaneFriction
math_p_numeric
[ { "content": "In a system called massprismplaneentity_0, a block of mass 2.6 kg rests on the left side a movable prism of mass 4.8 Kg. The prism makes an angle 60 degrees with the plane, which in turn makes an angle 0.0 degrees with horizontal. A string connected to the left side of the prism in 'massprismplane...
math
{ "ground_truth": "0.12509096370532005", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 345, "json_index": null, "split": "test" }
345
BasicCollision
math_p_numeric
[ { "content": "A smooth table is inclined at an angle 40.18 degrees with the horizontal. There are multiple systems on this table. In a system called 'complexcollisionplane_0.mass-0', a block of mass 1.0 kg is placed at -5.71 m on the table. It is initially moving with a velocity of -0.56 m/s. In a system called...
math
{ "ground_truth": "67.7586755955964", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 346, "json_index": null, "split": "test" }
346
IPhOProjectile
math_p_numeric
[ { "content": "In a setup, a ball of mass 1.0 kg is thrown vertically upward. The ball is launched from an initial height of 1.89 m from the ground and it has an initial speed of 1.65 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball an...
math
{ "ground_truth": "5.083828947401042", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 348, "json_index": null, "split": "test" }
348
BasicInclinedPlaneFriction
math_p_numeric
[ { "content": "In a system called 'twosidemassplane_0', a block of mass 1.0 kg rests on a plane inclined at an angle of 0 degrees. A string connected to the left side of the block in 'twosidemassplane_0' runs parallel to the plane to wrap around a pulley on the left side of the plane, and extends outward to conn...
math
{ "ground_truth": "1.0683734528257047", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 349, "json_index": null, "split": "test" }
349
IPhOPulley
math_p_numeric
[ { "content": "In a system called 'massboxplaneentity_0', a long movable box of mass 1.17 kg rests on a plane inclined at 2.98 degrees. A small block of mass 0.68 kg is placed on its top, allowing it to slide freely on the box. A pulley is fixed to the right edge of the box. A rope is attached to the right side ...
math
{ "ground_truth": "-0.014797584992155919", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 350, "json_index": null, "split": "test" }
350
BasicCollision
math_p_numeric
[ { "content": "In a system called 'twodcollisionplane_0', a smooth table (XY plane) has 3 spheres on it with the following properties (position and velocity are relative to the table): | Sphere | Mass (kg) | Initial Position (m) | Initial Velocity (m/s) | Radius (m) | |----------|-------------|------------------...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 351, "json_index": null, "split": "test" }
351
IPhOOrbitalMotion
math_p_numeric
[ { "content": "In a planetary system, a star with mass 3.34 M and radius 0.88 R is at the center. 1 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------...
math
{ "ground_truth": "2.553581693088454", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 352, "json_index": null, "split": "test" }
352
BasicPulley
math_p_numeric
[ { "content": "In a system called 'masswithfixedpulley_1', a block of mass 2.1 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_1' extends outward to wrap around the movable pulley in 'masswithmova...
math
{ "ground_truth": "0.20140886646006334", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 353, "json_index": null, "split": "test" }
353
IPhOOrbitalMotion
math_p_numeric
[ { "content": "In a planetary system, a star with mass 3.06 M and radius 1.02 R is at the center. 2 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------...
math
{ "ground_truth": "3.992007021594114", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 354, "json_index": null, "split": "test" }
354
BasicCollision
math_p_numeric
[ { "content": "In a system called 'twodcollisionplane_0', a smooth table (XY plane) has 2 spheres on it with the following properties (position and velocity are relative to the table): | Sphere | Mass (kg) | Initial Position (m) | Initial Velocity (m/s) | Radius (m) | |----------|-------------|------------------...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 355, "json_index": null, "split": "test" }
355
IPhOElectroMagnetic
math_p_numeric
[ { "content": "A charged particle with charge 2.77 C and mass 0.67 kg is initially launched from origin in the space. It has an initial velocity of -0.63 m/s in the x-direction and 1.09 m/s in the y-direction. There is a uniform electric field of strength 0.22 along the XY plane, making an angle of 296.15 degree...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 356, "json_index": null, "split": "test" }
356
Rotation
math_p_numeric
[ { "content": "A pendulum with a rope length of 0.79 m is attached to a fixed point in the ceiling on one end and a bob of mass 5.47 kg on the other end. The bob has an initial velocity of (0.81, -0.97) m/s in the horizontal plane, and the rope initially makes an angle of 33.65 degrees with the vertical. What is...
math
{ "ground_truth": "20.70169899395249", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 357, "json_index": null, "split": "test" }
357
IPhOProjectile
math_p_numeric
[ { "content": "In a setup, a ball of mass 1.0 kg is thrown horizontaly. The ball is launched from an initial height of 1.66 m from the ground and it has an initial speed of 1.31 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball and the ...
math
{ "ground_truth": "3.369288394531501", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 358, "json_index": null, "split": "test" }
358
RigidBodyRotation
math_p_numeric
[ { "content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A bar called 'bar_0' has a mass of 2.41 kg. It has a length of 0.76, width of 0.12, and heigh...
math
{ "ground_truth": "6.9130051201141525", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 360, "json_index": null, "split": "test" }
360
RigidBodyRotation
math_p_numeric
[ { "content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A bar called 'bar_0' has a mass of 2.41 kg. It has a length of 0.76, width of 0.12, and heigh...
math
{ "ground_truth": "0.49409488676074254", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 361, "json_index": null, "split": "test" }
361
BasicCollision
math_p_numeric
[ { "content": "A smooth table is inclined at an angle 26.78 degrees with the horizontal. There are multiple systems on this table. A spring (initially relaxed) fixed on its right end, extends to the left to -8.56 m on the table. It has a stiffness of 119.64 N/m, and a natural length of 0.28 m. A block of mass 1....
math
{ "ground_truth": "663.3067210314628", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 362, "json_index": null, "split": "test" }
362
IPhOOrbitalMotion
math_p_numeric
[ { "content": "In a planetary system, a star with mass 4.42 M and radius 1.12 R is at the center. 1 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------...
math
{ "ground_truth": "0.9233629619224656", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 363, "json_index": null, "split": "test" }
363
BasicPulley
math_p_numeric
[ { "content": "In a system called 'masswithfixedpulley_0', a block of mass 2.5 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_0' extends outward to wrap around the movable pulley in 'masswithmova...
math
{ "ground_truth": "13.381222320625788", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 364, "json_index": null, "split": "test" }
364
BasicCollision
math_p_numeric
[ { "content": "A smooth table is inclined at an angle 40.18 degrees with the horizontal. There are multiple systems on this table. In a system called 'complexcollisionplane_0.mass-0', a block of mass 1.0 kg is placed at -5.71 m on the table. It is initially moving with a velocity of -0.56 m/s. In a system called...
math
{ "ground_truth": "16.528953962434493", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 365, "json_index": null, "split": "test" }
365
IPhOPulley
math_p_numeric
[ { "content": "In a system called 'massboxplaneentity_0', a long movable box of mass 1.68 kg rests on a plane inclined at -11.14 degrees. A small block of mass 0.85 kg is placed on its top, allowing it to slide freely on the box. A pulley is fixed to the right edge of the box. A rope is attached to the right sid...
math
{ "ground_truth": "0.15573920638534022", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 366, "json_index": null, "split": "test" }
366
Rotation
math_p_numeric
[ { "content": "A pendulum with a rope length of 0.97 m is attached to a fixed point in the ceiling on one end and a bob of mass 8.99 kg on the other end. The bob has an initial velocity of (0.85, -0.36) m/s in the horizontal plane, and the rope initially makes an angle of 52.48 degrees with the vertical. What is...
math
{ "ground_truth": "-9.218412468762605", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 367, "json_index": null, "split": "test" }
367
Rotation
math_p_numeric
[ { "content": "A pendulum with a rope length of 0.79 m is attached to a fixed point in the ceiling on one end and a bob of mass 2.09 kg on the other end. The bob has an initial velocity of (-0.14, 0.94) m/s in the horizontal plane, and the rope initially makes an angle of 24.05 degrees with the vertical. What is...
math
{ "ground_truth": "1.479118619174258e-17", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 368, "json_index": null, "split": "test" }
368
BasicPulley
math_p_numeric
[ { "content": "In a system called 'masswithfixedpulley_0', a block of mass 2.5 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_0' extends outward to wrap around the movable pulley in 'masswithmova...
math
{ "ground_truth": "26.06731620903692", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 369, "json_index": null, "split": "test" }
369
RigidBodyRotation
math_p_numeric
[ { "content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A cylinder called 'cylinder_0' has a mass of 1.63 kg. It has a radius of 0.19 and a height of...
math
{ "ground_truth": "0.041389374322644126", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 370, "json_index": null, "split": "test" }
370
RigidBodyRotation
math_p_numeric
[ { "content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A bar called 'bar_0' has a mass of 2.66 kg. It has a length of 0.73, width of 0.1, and height...
math
{ "ground_truth": "0.3414074116613976", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 371, "json_index": null, "split": "test" }
371
IPhOSpringMass
math_p_numeric
[ { "content": "In a SpringMass system, 2 blocks are placed at -1.33 and 1.3 m on the table. They have masses 2.56 and 2.07 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 188.05 N/m respectively. The natural length of these springs ar...
math
{ "ground_truth": "6.617444900424222e-24", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 372, "json_index": null, "split": "test" }
372
RigidBodyRotation
math_p_numeric
[ { "content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A cylinder called 'cylinder_0' has a mass of 2.54 kg. It has a radius of 0.24 and a height of...
math
{ "ground_truth": "0.31677724002642266", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 373, "json_index": null, "split": "test" }
373
IPhOOrbitalMotion
math_p_numeric
[ { "content": "In a planetary system, a star with mass 4.4 M and radius 0.78 R is at the center. 2 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|-----------...
math
{ "ground_truth": "-0.028794540141252847", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 374, "json_index": null, "split": "test" }
374
IPhOElectroMagnetic
math_p_numeric
[ { "content": "A charged particle with charge 2.48 C and mass 1.38 kg is initially launched from origin in the space. It has an initial velocity of 0.26 m/s in the x-direction and 0.66 m/s in the y-direction. There is a uniform electric field of strength 0.46 along the XY plane, making an angle of 353.98 degrees...
math
{ "ground_truth": "8.788231317656287", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 375, "json_index": null, "split": "test" }
375
Rotation
math_p_numeric
[ { "content": "A pendulum with a rope length of 1.64 m is attached to a fixed point in the ceiling on one end and a bob of mass 5.91 kg on the other end. The bob has an initial velocity of (-0.76, -0.0) m/s in the horizontal plane, and the rope initially makes an angle of 86.23 degrees with the vertical. What is...
math
{ "ground_truth": "107.32987959456482", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 378, "json_index": null, "split": "test" }
378
RigidBodyRotation
math_p_numeric
[ { "content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A cylinder called 'cylinder_0' has a mass of 2.54 kg. It has a radius of 0.24 and a height of...
math
{ "ground_truth": "-0.18448038863071833", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 379, "json_index": null, "split": "test" }
379
BasicPulley
math_p_numeric
[ { "content": "In a system called 'masswithfixedpulley_0', a block of mass 1.0 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_0' extends outward to connect to the block in 'masswithfixedpulley_1'...
math
{ "ground_truth": "9.809999999993055", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 380, "json_index": null, "split": "test" }
380
Rotation
math_p_numeric
[ { "content": "A pendulum with a rope length of 0.79 m is attached to a fixed point in the ceiling on one end and a bob of mass 5.47 kg on the other end. The bob has an initial velocity of (0.81, -0.97) m/s in the horizontal plane, and the rope initially makes an angle of 33.65 degrees with the vertical. What is...
math
{ "ground_truth": "-8.881784197001252e-16", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 381, "json_index": null, "split": "test" }
381
BasicCollision
math_p_numeric
[ { "content": "A smooth table is inclined at an angle 15.76 degrees with the horizontal. There are multiple systems on this table. In a system called 'complexcollisionplane_0.mass-0', a block of mass 1.46 kg is placed at -8.93 m on the table. It is initially moving with a velocity of -0.11 m/s. In a system calle...
math
{ "ground_truth": "53.778753584794124", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 382, "json_index": null, "split": "test" }
382
IPhOOrbitalMotion
math_p_numeric
[ { "content": "In a planetary system, a star with mass 3.06 M and radius 1.02 R is at the center. 2 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------...
math
{ "ground_truth": "8.0347016346673", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 383, "json_index": null, "split": "test" }
383
IPhOSpringMass
math_p_numeric
[ { "content": "In a SpringMass system, 3 blocks are placed at -1.54, 0.48 and 1.42 m on the table. They have masses 1.61, 2.95 and 1.7 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 160.72 and 56.45 N/m respectively. The natural leng...
math
{ "ground_truth": "1.059442389037451e-08", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 384, "json_index": null, "split": "test" }
384
BasicPulley
math_p_numeric
[ { "content": "In a system called 'masswithfixedpulley_1', a block of mass 2.0 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_1' extends outward to wrap around the movable pulley in 'masswithmova...
math
{ "ground_truth": "14.70857142856571", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 385, "json_index": null, "split": "test" }
385
IPhOElectroMagnetic
math_p_numeric
[ { "content": "A charged particle with charge -1.34 C and mass 1.31 kg is initially launched from origin in the space. It has an initial velocity of -1.61 m/s in the x-direction and -1.18 m/s in the y-direction. There is a uniform electric field of strength 1.37 along the XY plane, making an angle of 334.1 degre...
math
{ "ground_truth": "-0.3311188932203638", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 387, "json_index": null, "split": "test" }
387
Rotation
math_p_numeric
[ { "content": "A pendulum with a rope length of 1.64 m is attached to a fixed point in the ceiling on one end and a bob of mass 5.91 kg on the other end. The bob has an initial velocity of (-0.76, -0.0) m/s in the horizontal plane, and the rope initially makes an angle of 86.23 degrees with the vertical. What is...
math
{ "ground_truth": "-78.63665816705405", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 388, "json_index": null, "split": "test" }
388
BasicInclinedPlaneFriction
math_p_numeric
[ { "content": "In a system called massprismplaneentity_0, a block of mass 2.6 kg rests on the left side a movable prism of mass 4.8 Kg. The prism makes an angle 60 degrees with the plane, which in turn makes an angle 0.0 degrees with horizontal. A string connected to the left side of the prism in 'massprismplane...
math
{ "ground_truth": "56.75708846794962", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 389, "json_index": null, "split": "test" }
389
BasicPulley
math_p_numeric
[ { "content": "In a system called 'masswithreversedmovablepulley_0', a movable pulley of mass 0.26 kg supports two blocks of masses 7.04 kg and 7.33 kg hanging on its left and right sides respectively, pulling the pulley down. The string that connects the movable pulley in 'masswithreversedmovablepulley_0' to an...
math
{ "ground_truth": "116.5627621696918", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 390, "json_index": null, "split": "test" }
390
Rotation
math_p_numeric
[ { "content": "A pendulum with a rope length of 1.06 m is attached to a fixed point in the ceiling on one end and a bob of mass 0.62 kg on the other end. The bob has an initial velocity of (-0.67, -0.37) m/s in the horizontal plane, and the rope initially makes an angle of 47.52 degrees with the vertical. What i...
math
{ "ground_truth": "3.884573164739457", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 391, "json_index": null, "split": "test" }
391
BasicCollision
math_p_numeric
[ { "content": "A smooth table is inclined at an angle 2.93 degrees with the horizontal. There are multiple systems on this table. A spring (initially relaxed) fixed on its right end, extends to the left to -4.04 m on the table. It has a stiffness of 69.11 N/m, and a natural length of 0.12 m. A block of mass 1.0 ...
math
{ "ground_truth": "0.05901339184436862", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 392, "json_index": null, "split": "test" }
392
IPhOPulley
math_p_numeric
[ { "content": "In a system called 'massprismpulleyplane_0', a large movable prism of mass 16.26 kg rests on a plane inclined at 0.0 degrees. The prism is inclined at an angle of 60 degrees on the left side and 60 degrees on the right side. Two blocks of mass 2.96 kg and 1.93 kg are resting on the left and right ...
math
{ "ground_truth": "151.07882415121406", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 393, "json_index": null, "split": "test" }
393
IPhOProjectile
math_p_numeric
[ { "content": "In a setup, a ball of mass 1.0 kg is thrown vertically upward. The ball is launched from an initial height of 1.89 m from the ground and it has an initial speed of 1.65 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball an...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 394, "json_index": null, "split": "test" }
394
IPhOProjectile
math_p_numeric
[ { "content": "In a setup, a ball of mass 1.0 kg is thrown horizontaly. The ball is launched from an initial height of 1.99 m from the ground and it has an initial speed of 1.07 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball and the ...
math
{ "ground_truth": "3.296747883664601", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 395, "json_index": null, "split": "test" }
395
Rotation
math_p_numeric
[ { "content": "A pendulum with a rope length of 1.06 m is attached to a fixed point in the ceiling on one end and a bob of mass 0.62 kg on the other end. The bob has an initial velocity of (-0.67, -0.37) m/s in the horizontal plane, and the rope initially makes an angle of 47.52 degrees with the vertical. What i...
math
{ "ground_truth": "2.9696485580734196e-16", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 396, "json_index": null, "split": "test" }
396
IPhOElectroMagnetic
math_p_numeric
[ { "content": "A charged particle with charge -2.72 C and mass 0.74 kg is initially launched from origin in the space. It has an initial velocity of 0.37 m/s in the x-direction and 1.21 m/s in the y-direction. There is a uniform magnetic field of strength 0.21 along the +Z axis. The field is effective in a recta...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 397, "json_index": null, "split": "test" }
397
IPhOPulley
math_p_numeric
[ { "content": "In a system called 'massboxplaneentity_0', a long movable box of mass 1.15 kg rests on a plane inclined at -6.66 degrees. A small block of mass 0.71 kg is placed on its top, allowing it to slide freely on the box. A pulley is fixed to the right edge of the box. A rope is attached to the right side...
math
{ "ground_truth": "0.0065842122894670015", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 398, "json_index": null, "split": "test" }
398
BasicPulley
math_p_numeric
[ { "content": "In a system called 'masswithreversedmovablepulley_0', a movable pulley of mass 0.26 kg supports two blocks of masses 7.04 kg and 7.33 kg hanging on its left and right sides respectively, pulling the pulley down. The string that connects the movable pulley in 'masswithreversedmovablepulley_0' to an...
math
{ "ground_truth": "72.12746777022943", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 399, "json_index": null, "split": "test" }
399
IPhOProjectile
math_p_numeric
[ { "content": "In a setup, a ball of mass 1.0 kg is thrown vertically upward. The ball is launched from an initial height of 1.73 m from the ground and it has an initial speed of 2.29 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball an...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 400, "json_index": null, "split": "test" }
400
Rotation
math_p_numeric
[ { "content": "A pendulum with a rope length of 1.67 m is attached to a fixed point in the ceiling on one end and a bob of mass 7.17 kg on the other end. The bob has an initial velocity of (-0.08, 0.16) m/s in the horizontal plane, and the rope initially makes an angle of 30.97 degrees with the vertical. What is...
math
{ "ground_truth": "-15.892164049567523", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 401, "json_index": null, "split": "test" }
401
IPhOSpringMass
math_p_numeric
[ { "content": "In a SpringMass system, 3 blocks are placed at -0.81, 0.36 and 1.43 m on the table. They have masses 2.57, 1.01 and 2.37 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 64.72 and 104.21 N/m respectively. The natural len...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 402, "json_index": null, "split": "test" }
402
BasicPulley
math_p_numeric
[ { "content": "In a system called 'masswithfixedpulley_0', a block of mass 1.0 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_0' extends outward to connect to the block in 'masswithfixedpulley_1'...
math
{ "ground_truth": "1.5844210095372624e-05", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 403, "json_index": null, "split": "test" }
403
IPhOOrbitalMotion
math_p_numeric
[ { "content": "In a planetary system, a star with mass 3.61 M and radius 1.22 R is at the center. 2 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------...
math
{ "ground_truth": "9.869495050545925", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 404, "json_index": null, "split": "test" }
404
BasicInclinedPlaneFriction
math_p_numeric
[ { "content": "In a system called 'twosidemassplane_0', a block of mass 1.0 kg rests on a plane inclined at an angle of 0 degrees. A string connected to the left side of the block in 'twosidemassplane_0' runs parallel to the plane to wrap around a pulley on the left side of the plane, and extends outward to conn...
math
{ "ground_truth": "25.042001437408253", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 405, "json_index": null, "split": "test" }
405
IPhOOrbitalMotion
math_p_numeric
[ { "content": "In a planetary system, a star with mass 3.06 M and radius 1.02 R is at the center. 2 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------...
math
{ "ground_truth": "4.228848312813451", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 407, "json_index": null, "split": "test" }
407
RigidBodyRotation
math_p_numeric
[ { "content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A cylinder called 'cylinder_0' has a mass of 2.54 kg. It has a radius of 0.24 and a height of...
math
{ "ground_truth": "0.18301763513002525", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 408, "json_index": null, "split": "test" }
408
RigidBodyRotation
math_p_numeric
[ { "content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A cylinder called 'cylinder_0' has a mass of 2.01 kg. It has a radius of 0.21 and a height of...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 409, "json_index": null, "split": "test" }
409
IPhOProjectile
math_p_numeric
[ { "content": "In a setup, a ball of mass 1.0 kg is thrown horizontaly. The ball is launched from an initial height of 1.67 m from the ground and it has an initial speed of 1.77 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball and the ...
math
{ "ground_truth": "3.36736531405261", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 411, "json_index": null, "split": "test" }
411
IPhOProjectile
math_p_numeric
[ { "content": "In a setup, a ball of mass 1.0 kg is thrown vertically downward. The ball is launched from an initial height of 1.17 m from the ground and it has an initial speed of 2.31 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball ...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 412, "json_index": null, "split": "test" }
412
IPhOOrbitalMotion
math_p_numeric
[ { "content": "In a planetary system, a star with mass 3.64 M and radius 0.89 R is at the center. 1 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------...
math
{ "ground_truth": "5.311482554700472", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 413, "json_index": null, "split": "test" }
413
BasicCollision
math_p_numeric
[ { "content": "In a system called 'twodcollisionplane_0', a smooth table (XY plane) has 3 spheres on it with the following properties (position and velocity are relative to the table): | Sphere | Mass (kg) | Initial Position (m) | Initial Velocity (m/s) | Radius (m) | |----------|-------------|------------------...
math
{ "ground_truth": "0.09589493678419984", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 414, "json_index": null, "split": "test" }
414
BasicPulley
math_p_numeric
[ { "content": "In a system called 'masswithreversedmovablepulley_0', a movable pulley of mass 0.6 kg supports two blocks of masses 5.67 kg and 8.28 kg hanging on its left and right sides respectively, pulling the pulley down. The string that connects the movable pulley in 'masswithreversedmovablepulley_0' to an ...
math
{ "ground_truth": "18.99959239221616", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 415, "json_index": null, "split": "test" }
415
BasicCollision
math_p_numeric
[ { "content": "A smooth table is inclined at an angle 8.12 degrees with the horizontal. There are multiple systems on this table. A spring (initially relaxed) fixed on its right end, extends to the left to -5.83 m on the table. It has a stiffness of 74.11 N/m, and a natural length of 0.23 m. A block of mass 1.0 ...
math
{ "ground_truth": "-5.204170427930421e-18", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 416, "json_index": null, "split": "test" }
416
IPhOOrbitalMotion
math_p_numeric
[ { "content": "In a planetary system, a star with mass 3.56 M and radius 0.82 R is at the center. 1 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------...
math
{ "ground_truth": "1.644901095048533", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 418, "json_index": null, "split": "test" }
418
Rotation
math_p_numeric
[ { "content": "A pendulum with a rope length of 1.37 m is attached to a fixed point in the ceiling on one end and a bob of mass 0.52 kg on the other end. The bob has an initial velocity of (0.54, 0.51) m/s in the horizontal plane, and the rope initially makes an angle of 76.26 degrees with the vertical. What is ...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 419, "json_index": null, "split": "test" }
419
IPhOProjectile
math_p_numeric
[ { "content": "In a setup, a ball of mass 1.0 kg is thrown vertically upward. The ball is launched from an initial height of 1.06 m from the ground and it has an initial speed of 2.49 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball an...
math
{ "ground_truth": "1.1987206066560687", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 420, "json_index": null, "split": "test" }
420
RigidBodyRotation
math_p_numeric
[ { "content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A bar called 'bar_0' has a mass of 2.95 kg. It has a length of 0.82, width of 0.14, and heigh...
math
{ "ground_truth": "1.8679146006474958", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 421, "json_index": null, "split": "test" }
421
IPhOSpringMass
math_p_numeric
[ { "content": "In a SpringMass system, 3 blocks are placed at -0.78, -0.5 and 0.83 m on the table. They have masses 0.86, 2.94 and 2.95 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 52.96 and 97.54 N/m respectively. The natural leng...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 422, "json_index": null, "split": "test" }
422
RigidBodyRotation
math_p_numeric
[ { "content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A bar called 'bar_0' has a mass of 3.0 kg. It has a length of 0.92, width of 0.1, and height ...
math
{ "ground_truth": "9.072708148103757", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 423, "json_index": null, "split": "test" }
423
Rotation
math_p_numeric
[ { "content": "A pendulum with a rope length of 0.97 m is attached to a fixed point in the ceiling on one end and a bob of mass 8.99 kg on the other end. The bob has an initial velocity of (0.85, -0.36) m/s in the horizontal plane, and the rope initially makes an angle of 52.48 degrees with the vertical. What is...
math
{ "ground_truth": "7.545510997978755", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 424, "json_index": null, "split": "test" }
424
RigidBodyRotation
math_p_numeric
[ { "content": "In a system, there are 2 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A cylinder called 'cylinder_1' has a mass of 1.27 kg. It has a radius of 0.28 and a height of...
math
{ "ground_truth": "13.124109776371622", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 425, "json_index": null, "split": "test" }
425
IPhOOrbitalMotion
math_p_numeric
[ { "content": "In a planetary system, a star with mass 3.34 M and radius 0.91 R is at the center. 2 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------...
math
{ "ground_truth": "0.8984878826778576", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 426, "json_index": null, "split": "test" }
426
BasicInclinedPlaneFriction
math_p_numeric
[ { "content": "In a system called massprismplaneentity_0, a block of mass 0.6 kg rests on the left side a movable prism of mass 2.6 Kg. The prism makes an angle 60 degrees with the plane, which in turn makes an angle 0.0 degrees with horizontal. A string connected to the left side of the prism in 'massprismplane...
math
{ "ground_truth": "-51.39939206008435", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 427, "json_index": null, "split": "test" }
427
BasicInclinedPlaneFriction
math_p_numeric
[ { "content": "In a system called 'twosidemassplane_0', a block of mass 1.0 kg rests on a plane inclined at an angle of 0 degrees. A string connected to the left side of the block in 'twosidemassplane_0' runs parallel to the plane to wrap around a pulley on the left side of the plane, and extends outward to conn...
math
{ "ground_truth": "4.0593699009645784e-15", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 428, "json_index": null, "split": "test" }
428
IPhOPulley
math_p_numeric
[ { "content": "In a system called 'massboxplaneentity_0', a long movable box of mass 1.42 kg rests on a plane inclined at 11.36 degrees. A small block of mass 0.53 kg is placed on its top, allowing it to slide freely on the box. A pulley is fixed to the right edge of the box. A rope is attached to the right side...
math
{ "ground_truth": "-0.04170554835571529", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 430, "json_index": null, "split": "test" }
430
IPhOElectroMagnetic
math_p_numeric
[ { "content": "A charged particle with charge 2.48 C and mass 1.38 kg is initially launched from origin in the space. It has an initial velocity of 0.26 m/s in the x-direction and 0.66 m/s in the y-direction. There is a uniform electric field of strength 0.46 along the XY plane, making an angle of 353.98 degrees...
math
{ "ground_truth": "0.9581108002768709", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 431, "json_index": null, "split": "test" }
431
IPhOSpringMass
math_p_numeric
[ { "content": "In a SpringMass system, 3 blocks are placed at -0.83, -0.43 and 0.98 m on the table. They have masses 1.83, 2.15 and 2.06 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 78.84 and 109.73 N/m respectively. The natural le...
math
{ "ground_truth": "7.794974183538236e-06", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 432, "json_index": null, "split": "test" }
432
IPhOSpringMass
math_p_numeric
[ { "content": "In a SpringMass system, 4 blocks are placed at -1.02, -0.83, 0.29 and 1.62 m on the table. They have masses 0.9, 0.94, 1.73 and 2.03 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 139.82, 112.3 and 78.2 N/m respectivel...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 433, "json_index": null, "split": "test" }
433
BasicPulley
math_p_numeric
[ { "content": "In a system called 'masswithreversedmovablepulley_0', a movable pulley of mass 0.26 kg supports two blocks of masses 7.04 kg and 7.33 kg hanging on its left and right sides respectively, pulling the pulley down. The string that connects the movable pulley in 'masswithreversedmovablepulley_0' to an...
math
{ "ground_truth": "92.4491814288751", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 434, "json_index": null, "split": "test" }
434
IPhOOrbitalMotion
math_p_numeric
[ { "content": "In a planetary system, a star with mass 3.45 M and radius 1.14 R is at the center. 2 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------...
math
{ "ground_truth": "4.53341726386828", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 436, "json_index": null, "split": "test" }
436
Rotation
math_p_numeric
[ { "content": "A pendulum with a rope length of 1.1 m is attached to a fixed point in the ceiling on one end and a bob of mass 7.82 kg on the other end. The bob has an initial velocity of (-0.38, 0.06) m/s in the horizontal plane, and the rope initially makes an angle of 63.01 degrees with the vertical. What is ...
math
{ "ground_truth": "0.03128", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 437, "json_index": null, "split": "test" }
437
Rotation
math_p_numeric
[ { "content": "A pendulum with a rope length of 1.63 m is attached to a fixed point in the ceiling on one end and a bob of mass 6.0 kg on the other end. The bob has an initial velocity of (0.2, -0.32) m/s in the horizontal plane, and the rope initially makes an angle of 30.44 degrees with the vertical. What is t...
math
{ "ground_truth": "7.5996362702683715", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 438, "json_index": null, "split": "test" }
438
IPhOOrbitalMotion
math_p_numeric
[ { "content": "In a planetary system, a star with mass 3.72 M and radius 1.01 R is at the center. 1 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------...
math
{ "ground_truth": "5.6830457047516", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 439, "json_index": null, "split": "test" }
439
BasicCollision
math_p_numeric
[ { "content": "In a system called 'twodcollisionplane_0', a smooth table (XY plane) has 2 spheres on it with the following properties (position and velocity are relative to the table): | Sphere | Mass (kg) | Initial Position (m) | Initial Velocity (m/s) | Radius (m) | |----------|-------------|------------------...
math
{ "ground_truth": "1.963101041622647", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 440, "json_index": null, "split": "test" }
440
BasicPulley
math_p_numeric
[ { "content": "In a system called 'masswithfixedpulley_0', a block of mass 1.9 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_0' extends outward to connect to the block in 'masswithfixedpulley_1'...
math
{ "ground_truth": "-29.53706972116081", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 441, "json_index": null, "split": "test" }
441
IPhOProjectile
math_p_numeric
[ { "content": "In a setup, a ball of mass 1.0 kg is thrown vertically upward. The ball is launched from an initial height of 1.73 m from the ground and it has an initial speed of 2.29 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball an...
math
{ "ground_truth": "0.5762198317879088", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 443, "json_index": null, "split": "test" }
443
RigidBodyRotation
math_p_numeric
[ { "content": "In a system, there are 2 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A cylinder called 'cylinder_1' has a mass of 1.27 kg. It has a radius of 0.28 and a height of...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 444, "json_index": null, "split": "test" }
444
IPhOElectroMagnetic
math_p_numeric
[ { "content": "A charged particle with charge -1.99 C and mass 1.08 kg is initially launched from origin in the space. It has an initial velocity of -0.52 m/s in the x-direction and -0.66 m/s in the y-direction. There is a uniform magnetic field of strength 0.83 along the +Z axis. The field is effective in an an...
math
{ "ground_truth": "1.299503250232004", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 445, "json_index": null, "split": "test" }
445
IPhOProjectile
math_p_numeric
[ { "content": "In a setup, a ball of mass 1.0 kg is thrown vertically upward. The ball is launched from an initial height of 1.33 m from the ground and it has an initial speed of 1.89 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball an...
math
{ "ground_truth": "2.06848457804032", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 446, "json_index": null, "split": "test" }
446
IPhOOrbitalMotion
math_p_numeric
[ { "content": "In a planetary system, a star with mass 3.45 M and radius 1.14 R is at the center. 2 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------...
math
{ "ground_truth": "3.432291980424734", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 447, "json_index": null, "split": "test" }
447
IPhOProjectile
math_p_numeric
[ { "content": "In a setup, a ball of mass 1.0 kg is thrown vertically upward. The ball is launched from an initial height of 1.08 m from the ground and it has an initial speed of 2.91 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball an...
math
{ "ground_truth": "1.8410981465177738", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 448, "json_index": null, "split": "test" }
448
IPhOElectroMagnetic
math_p_numeric
[ { "content": "A charged particle with charge -1.34 C and mass 1.31 kg is initially launched from origin in the space. It has an initial velocity of -1.61 m/s in the x-direction and -1.18 m/s in the y-direction. There is a uniform electric field of strength 1.37 along the XY plane, making an angle of 334.1 degre...
math
{ "ground_truth": "6.823521816851462e-13", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 450, "json_index": null, "split": "test" }
450
IPhOSpringMass
math_p_numeric
[ { "content": "In a SpringMass system, 3 blocks are placed at -0.83, -0.43 and 0.98 m on the table. They have masses 1.83, 2.15 and 2.06 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 78.84 and 109.73 N/m respectively. The natural le...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 451, "json_index": null, "split": "test" }
451
IPhOProjectile
math_p_numeric
[ { "content": "In a setup, a ball of mass 1.0 kg is thrown horizontaly. The ball is launched from an initial height of 1.49 m from the ground and it has an initial speed of 2.01 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball and the ...
math
{ "ground_truth": "4.36483451543351", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 452, "json_index": null, "split": "test" }
452
IPhOSpringMass
math_p_numeric
[ { "content": "In a SpringMass system, 3 blocks are placed at -0.81, 0.36 and 1.43 m on the table. They have masses 2.57, 1.01 and 2.37 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 64.72 and 104.21 N/m respectively. The natural len...
math
{ "ground_truth": "2.9817521026413524e-08", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 453, "json_index": null, "split": "test" }
453
IPhOSpringMass
math_p_numeric
[ { "content": "In a SpringMass system, 3 blocks are placed at -1.21, 0.14 and 0.95 m on the table. They have masses 2.24, 2.69 and 2.58 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 75.47 and 185.38 N/m respectively. The natural len...
math
{ "ground_truth": "0.0", "style": "rule" }
{ "answer_type": null, "file_name": null, "given_variable_mapping": null, "index": 454, "json_index": null, "split": "test" }
454