datavorous/entrance-exam-dataset huggingface dataset:
A particle starts from origin at t = 0 with a velocity 5.0 î m/s and moves in x-y plane under action of a force which produces a constant acceleration of (3.0i ɵ+2.0j ɵ ) m/s 2 . What is the y-coordinate of the particle at the instant its x-coordinate is 84 m ?

Options:
A 34m
B 40m
C 44m
D 36m

The correct answer is:
36m

Solution:
Correct Option is : (D)
36m

Topic: Chemistry, Motion In Two Dimensions, NEET
A particle starts from rest and traverses a distance 2x with uniform acceleration, then moves uniformly over a further distance 4x and finally comes to rest after moving a further distance 6x under uniform retardation. Assuming entire motion to be rectilinear motion, the ratio of average speed over the journey to the maximum speed on its way is

Options:
A 45
B 35
C 25
D 15

The correct answer is:
35

Solution:
Let t1,t2 and t3 be the time taken by the particles to cover the distance 2x, 4x and 6x respectively. Let v be the velocity of the particle at B ie, maximum velocity. The particle moves with uniform acceleration from A to B.
For motion from A to B.
Average velocity =0+v2=v2
Time taken, t1=2xv2
Particle moves with uniform retardation from C TO D, Vavg=0+v2=v2
Time taken ,t3=6x(v2)
Total time =t1+t2+t3
t=2xv2+4xv+6xv2=20xv
Average Velocity over = 6x+2x+4x20xv=35v
Required Ratio =AverageSpeedv=35

Topic: Physics, Motion In One Dimension, NEET
A particle starts from rest at t=0 and moves in a straight line with acceleration as shown in figure. The velocity of the particle at t=3 s is

Options:
A 2Â ms-1
B 4 ms-1
C 6Â ms-1
D 8Â ms-1

The correct answer is:
4 ms-1

Solution:
Velocity at 3s= total algebraic sum of area under the curve
vâ¡ = 4 × 2 - 4 × 1 = 4 m/s

Topic: Physics, Units and Dimensions, NEET
A particle starts from the origin at t = 0 s with a velocity of 10.0 $\hat{j}$ m/s and moves in the x-y plane with a constant acceleration of $8\hat{i}+2\hat{j}$. At what time is the x- coordinate of the particle 16 m?

Options:
A 3 s
B 4 s
C 2 s
D 1s

The correct answer is:
2 s

Solution:
Correct Option is : (C)
2 s

Topic: Chemistry, Motion In Two Dimensions, NEET
A particle starts its motion from rest under the action of a constant force. If the distance covered in first $10 \mathrm{~s}$ is $\mathrm{s}_1$ and that covered in the first $20 \mathrm{~s}$ is $\mathrm{s}_2$, then

Options:
A $\mathrm{s}_2=2 \mathrm{~s}_1$
B $\mathrm{s}_2=3 \mathrm{~s}_1$
C $s_2=4 s_1$
D $s_2=s_1$

The correct answer is:
$s_2=4 s_1$

Solution:
Key Idea If the particle is moving in a straight line under the action of a constant force then distance covered $\mathrm{s}=\mathrm{ut}+\frac{1}{2}$ at $^2$.
Since the body start from rest $\mathrm{u}=0$
$\therefore \quad \mathrm{s}=\frac{1}{2} \mathrm{at}^2$
Now, $\quad \mathrm{s}_1=\frac{1}{2} \mathrm{a}(10)^2$
and
$$
\mathrm{s}_2=\frac{1}{2} \mathrm{a}(20)^2
$$
Dividing Eq. (i) and Eq. (ii), we get
$$
\begin{aligned}
\frac{\mathrm{s}_1}{\mathrm{~s}_2} & =\frac{(10)^2}{(20)^2} \\
\Rightarrow \quad s_2 & =4 \mathrm{~s}_1
\end{aligned}
$$

Topic: Physics, Motion In One Dimension, NEET, NEET 2009 (Screening)
A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S 1 and that covered in the first 20 seconds is S 2 , then:

Options:
A S 2  = 3 S 1
B S 2 â=â4 S 1
C S 2  =  S 1
D S 2  = 2 S 1

The correct answer is:
S 2  = 4 S 1

Solution:
Given:

uâ=â0â,â t 1 â=â10sâ,â t 2 â=â20s

Using the relation, Sâ=âut+ 1 2 a t 2

Acceleration being the same in two cases.

S 1 â=â 1 2 âaâÃâ t 1 2 â,â S 2 â=â 1 2 âaâÃâ t 2 2

â´â S 1 S 2 â=â ( t 1 t 2 ) 2 â=â ( 10 20 ) 2 â=â 1 4

S 2 â=â4 S 1

Topic: Physics, Motion In One Dimension, NEET
A particle starts oscillating simple harmonically from its equilibrium position with time period T. The ratio of KE and PE of the particle at the t=T/12 is

Options:
A 1:4
B 2:1
C 3:1
D 4:1

The correct answer is:
3:1

Solution:
When t=T12, then x=Asinâ¡2ÏTÃT12=A2
KE=12 mv2=12 mÏ2(A2-x2)
= 12 mÏ2A2-A24
= 3412 mÏ2A2
PE=12 mÏ2x2=1412 mÏ2A2
KEPE=31

Topic: Physics, Oscillations, NEET
A particle strikes elastically with another particle with velocity V . After collision, it moves with half the velocity in the same direction. Find the velocity of the second particle if it is initially at rest.

Options:
A 3V2
B V2
C V
D none of these

The correct answer is:
3V2

Solution:
We know that
v2→-v1→=eu1→-u2→
or v2→-v2=1v-0 (for an elastic collision e=1)
or v2=3V2

Topic: Physics, Work Power Energy, NEET
A particle strikes elastically with another particle with velocity V. After the collision, it moves with half the velocity in the same direction. Find the velocity of the second particle if it is initially at rest

Options:
A 3V2
B V2
C V
D none of these

The correct answer is:
3V2

Solution:
v2→-v1→=eu1→-u2→
or v2→-v2=1v-0
or v2=3v2

Topic: Physics, Center of Mass Momentum and Collision, NEET
A particle suspended from a vertical spring oscillates 10 times per second. At the highest point of oscillation, the spring becomes unstretched. Find the speed when the spring is stretched by 0.20 cm. Take, g=Ï2 m/s2

Options:
A 110.25 cm s-1
B 12.14 cm s-1
C 15.4 cm s-1
D 16.7 cm s-1

The correct answer is:
15.4 cm s-1

Solution:
When a spring is in equilibrium, its extension =mgk At the highest point of block, spring is in its natural length.
Hence, amplitude, A=mgk
Given, f=10 Hz
ω=2πf=20π rad s-1
∴ ω=km
On squaring both sides, we get
km=ω2
⇒ vmax=Aω
=mkgω=gωω2
=gω=π220π=π20 m s-1
∴ A=mgk=gω2
=π2400 π2=0.25100 m=0.25 cm
Now, when the extension is 0.20 cm, then displacement from the equilibrium position =0.25-0.20=0.05 cm
x=0.05 cm
∴ v=ωA2-x2
=20π0.252-0.052
=2π6 cm s-1
=15.4 cm s-1

Topic: Physics, Oscillations, NEET
A particle travels along the arc of a circle of radius r. Its speed depends on the distance travelled l as v=a l, where a is a constant. The angle Î± between the vectors of total acceleration and the velocity of the particle is

Options:
A Î±= tan â1( 2l r )
B Î± = cos â1 ( 2l r )
C Î± = sin â1 ( 2l r )
D Î± = cot â1 ( 2l r )

The correct answer is:
α= tan −1( 2l r )

Solution:
Let, when particle is at angular position θ then distance travelled =l
v=a l
But a t = dv dt = a 2 l dl dt = av 2 l = a 2 2
And a c = v 2 r =( a 2 l r )
Angle between anet & at :
α= tan −1 ( 2l r )

Topic: Physics, Laws of Motion, NEET
A particle undergoes a one-dimensional motion such that its velocity varies according to vx=βx-2n, where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x is given by

Options:
A -2nβ2x-2n-1
B -2nβ2x-4n-1
C -2nβ2x-2n+1
D -2nβ2x-4n+1

The correct answer is:
-2nβ2x-4n-1

Solution:
According to the question
a=vdvdx=vddxβx​-2n
=-2nβx-2n-1 βx-2n
=-2nβ2x-4n-1

Topic: Physics, Motion In One Dimension, NEET, NEET 2015 (Phase 1)
A particle with linear momentum of magnitude P is subjected to a force F=Kt K>0 which is directed along the direction of initial momentum. The time after which its linear momentum changes to 3P is

Options:
A 2PK
B 2PK
C 2KP
D 2KP

The correct answer is:
2PK

Solution:
F=dpdt⇒Kt=dpdt
∫P3PdP=∫0tKtdt⇒3P-P=Kt22⇒t=2PK

Topic: Physics, Rotational Motion, NEET
A particle with total energy $E$ is moving in a potential energy region $U(x)$. Motion of the particle is restricted to the region when:

Options:
A $U(x) < E$
B $U(x)=0$
C $U(x) \leq E$
D $U(x)>E$

The correct answer is:
$U(x) \leq E$

Solution:
We know that
$$
\begin{aligned}
E & =K \cdot E+P E \\
E & =K \cdot E .+V(n) \\
\Rightarrow \quad E-U(n) & =K . E . \\
& =\frac{1}{2} m v^2 \\
\Rightarrow \quad E & \geq V(n)
\end{aligned}
$$

Topic: Physics, Work Power Energy, NEET, NEET 2013 (Karnataka)
A particular force ( F ) applied on a wire increases its length by 2Ã10-3 m. To increase the wire's length by 4Ã10-3 m, the applied force will be

Options:
A 4F
B 3F
C 2F
D F

The correct answer is:
2F

Solution:
Y=FAlL=FÃLAÃl
⇒F∝l
F1F2=l1l2
â¹ FF2=2Ã10-34Ã10-3
F2=2F

Topic: Physics, Mechanical Properties of Solids, NEET
A particular hydrogen like atom has its ground state binding energy =122.4  eV. It is in ground state. Then,

Options:
A its atomic number is 5
B an electron of 90  eV can excite it
C an electron of kinetic energy 45.9  eV can be brought to almost rest by this atom
D an electron of kinetic energy nearly 2.6  eV may emerge from the atom when electron of kinetic energy 125  eV collides with this atom

The correct answer is:
an electron of kinetic energy nearly 2.6  eV may emerge from the atom when electron of kinetic energy 125  eV collides with this atom

Solution:
Ground state binding energy =13.6Ã z 2 ââeV
â z = 122.4 13.6 = 3
The first excitation energy
Î E = 13.6 Ã z 2 Ã 1 - 1 4 eV = 91.8 eV
K .E max =125â122.4=2.6ââeV
Hence, 90ââeV electron cannot excite it.

Topic: Physics, Atomic Physics, NEET
A particular mineral element P activates various enzymes, especially nitrate reductase. Identify P.

Options:
A Cu
B Mo
C Mg
D Mn

The correct answer is:
Mo

Solution:
Plants obtain Mo in the form of molybdate ions (MoO22+). It is a component of several enzymes, including nitrogenase and nitrate reductase, both of which participate in nitrogen metabolism.

Topic: Biology, Mineral Nutrition, NEET
A particular species of animals had three coat colors: white, yellow and black. A population of this species in Africa had more number of yellow animals and less number of white and black animals. After hundreds of years, the species evolved having very few yellow animals and more white and black animals. The white and black animals were almost similar in quantity. The type of natural selection seen in this example is

Options:
A Stabilising selection
B Directional selection
C Disruptive selection
D It could be both stabilising and disruptive selection

The correct answer is:
Disruptive selection

Solution:
There are three types of natural selection. The type of selection in which the median character becomes more in number is called stabilizing selection. The type of selection in which the number of individuals with a character at the extreme end of the spectrum is increased is called directional selection. The type of selection in which two characters at extreme ends of the spectrum increase in number, whereas the median character decreases in number is called disruptive selection.

Topic: Biology, Evolution, NEET
A particular station of All India Radio, New Delhi, broadcasts on a frequency of 1,368 kHz (kilo Hertz). The wavelength of the electromagnetic radiation emitted by the transmitter is [speed of light, c=3.0×108 ms-1]

Options:
A 219.3 m
B 219.2 m
C 2192 m
D 21.92 cm

The correct answer is:
219.3 m

Solution:
Wavelength λ=cv

λ=3×1081368×103

λ=219.298 m

λ≈219.3 m

Topic: Chemistry, Structure of Atom, NEET, NEET 2021
A pathological process that is observed in a malignant tumour is known as ____.

Options:
A dynastasis
B metastasis
C statis
D pseudostatis

The correct answer is:
metastasis

Solution:
A pathological process that is observed in malignant tumours is known as metastasis.

Topic: Biology, Human Health and Diseases, NEET
A patient blood smear shows the following picture. Which disease is the patient suffering from?

Options:
A Malaria
B Sickle cell anaemia
C Thalassemia
D AIDS

The correct answer is:
Malaria

Solution:
Malaria is caused by protozoan Plasmodium. It multiplies within the RBCs. The given slide shows Plasmodium parasites within the RBCs.

Topic: Biology, Human Health and Diseases, NEET
A patient brought to a hospital with myocardial infarction is normally immediately given

Options:
A penicillin
B streptokinase
C cyclosporin-A
D statins

The correct answer is:
streptokinase

Solution:
Streptokinase (SK), a protein secreted by several species of streptococci can bind and activate human plasminogen. It is used as an effective and inexpensive thrombolysis medication in some cases of myocardial infarction and pulmonary embolism.

Topic: Biology, Body Fluids and Circulation, NEET, NEET 2012 (Screening)
A patient brought to a hospital with myocardial infarction is normally immediately given:

Options:
A Streptokinase
B Cyclosporin-A
C Statins
D Penicillin

The correct answer is:
Streptokinase

Solution:
Streptokinase is an enzyme that is part of the medication group called fibrinolytics. This enzyme helps in activating human plasminogen and reduce plasmin. It is generally used as a thrombolysis medication in some cases of myocardial infarction. It is very effective and inexpensive. This enzyme is secreted by several species of Streptococci.

Topic: Biology, Microbes in Human Welfare, NEET
A patient brought to the hospital with myocardial infarction is immediately given

Options:
A penicillin
B statins
C streptokinase
D cyclosporin A

The correct answer is:
streptokinase

Solution:
Streptokinase produced by the bacterium Streptococcus and modified by genetic engineering is used as a ‘clot-buster’ for removing clots from the blood vessels of patients who have undergone myocardial infarction leading to a heart attack.

Topic: Biology, Microbes in Human Welfare, NEET
A patient comes to a doctor's clinic situated on the 6th floor by walking up the staircase. As soon as he reaches the clinic, the nurse records his blood pressure as 148/ 92 mm Hg. Which of these statements is surely correct?

Options:
A The patient has high blood pressure and is definitely having hypertension
B The patient has high blood pressure and is definitely not having hypertension
C The patient has high blood pressure but may or may not have hypertension
D The patient has high blood pressure due to coronary heart disease

The correct answer is:
The patient has high blood pressure but may or may not have hypertension

Solution:
Hypertension is a disease of sustained high blood pressure. The patient has to rest for some time and the blood pressure should be measured again. The patient will have hypertension if the blood pressure is high even after adequate rest.

Topic: Biology, Body Fluids and Circulation, NEET
A patient has developed a clot in his heart. Which of these enzymes can be used to bust this clot?

Options:
A Amylase
B Streptokinase
C Pectinase
D Protease

The correct answer is:
Streptokinase

Solution:
Microbes have been used for various welfare activities and also in production of various chemicals in industries. Certain examples of chemicals produced with the help of microbes are organic acids, alcohols, and certain enzymes. One such enzyme called Streptokinase is produced by Streptococcus bacteria and is genetically modified. This enzyme is used for dissolving the blood clots which have blocked the vessels of the patient leading to myocardial infarction.

Topic: Biology, Microbes in Human Welfare, NEET
A patient has met with a car accident and has lost a lot of blood. Choose the response that will compensate the most for the blood loss.

Options:
A Increased stroke volume.
B Increased heart rate.
C Decreased heart rate.
D Increased uptake of water in the collecting duct of the nephron.

The correct answer is:
Increased heart rate.

Solution:
Heart rate represents the speed at which the heart performs the function of pumping blood into the arteries. If a person has extensive blood loss, then the best compensatory response would be an increased heart rate. This is because if the heart rate increases, blood will be pumped into the arteries at a faster rate. Thus, the blood loss will be compensated faster.

Topic: Biology, Body Fluids and Circulation, NEET
A patient is diagnosed with internal bleeding, muscular pain, fever, anemia, blockage of intestinal passage. He is most likely suffering from

Options:
A Filariasis
B Amoebiasis
C Ascariasis
D Malaria

The correct answer is:
Ascariasis

Solution:
Ascariais is caused by Round worms. These belong to Phylum Aschelminthes. These are known as roundworms as they show presence of body cavity. These show well presence of organ system and hence digestive system is also complete. These can be free living or parasitic in nature. The parasites can be in ectoparasites or endoparasites depending on whether they are on the host or inside the host. In humans these cause intestinal infections. These block the passage of intestine as a result of which internal bleeding, muscle cramps, fever occurs.

Topic: Biology, Human Health and Diseases, NEET
A patient is generally advised to specially, consume more meat, lentils, milk and eggs in diet only when he suffers from:

Options:
A scurvy
B kwashiorkor
C rickets
D anaemia.

The correct answer is:
kwashiorkor

Solution:
Kwashiorkar is caused due to the deficiency of protein and meat, lentils, milk and eggs are rich sources of protein. Scurvy is caused due to deficiency of vitamin $\mathrm{C}$ whose sources are citrus fruit, tomatoes, peppers, leafy green vegetables. Deficiency of vitamin D (sources milk, egg yolk and liver) leads to rickets. Anaemia is caused due to deficiency of folic acid (sources yeast, liver, fish, green vegetables) or vitamin B, (sources - liver, eggs, meat, fish) or iron (egg yolk, spinach).
Related Theory
Marasmus is due to severe weight loss and muscle wasting due to lack of nutrition (protein) and calories while Kwashiorkor is due to edema due to water retention from lack of protein. Marasmic-kwashiorkor is a combination of muscle wasting and bilateral edema.

Topic: Biology, Digestion and Absorption, NEET, NEET 2005
A patient suffering from Down's syndrome was carefully examined. There were three 21 chromosomes in the patient. The sequence of all the genes and alleles present on two of the three 21st chromosomes were an exact match with the patient's mother while the third one was an exact match with the patient's father. Which of the following process was faulty to have produced this individual?

Options:
A Anaphase I in maternal meiosis
B Anaphase I in paternal meiosis
C Anaphase II in maternal meiosis
D Anaphase II in paternal meiosis

The correct answer is:
Anaphase II in maternal meiosis

Solution:
Down's syndrome is trisomy 21. It occurs due to non-disjunction of chromosomes during anaphase I of meiosis. Since the patient has two chromosomes from the mother, the failure of disjunction happened in anaphase I or anaphase II of maternal meiosis.
Since the genes and alleles are exacty the same, the non-disjunction would have happened at anaphase II because the sister chromatids will have the same genomic content. If the non-disjunction happens at anaphase I, then the genes or alleles would not have been exactly same.

Topic: Biology, Principles of Inheritance and Variation, NEET
A patient's blood report reads eosinophilia. He must be suffering from

Options:
A a bacterial infection of some kind
B a viral infection of some kind
C an allergy of some kind
D an immunodeficiency of some kind

The correct answer is:
an allergy of some kind

Solution:
Blood consists of plasma and cellular components. Cellular components include Erythrocytes, Leucocytes and Thrombocytes. Leucocytes can be Granulocytes and Agranulocytes depending on presence and absence of granules. Granulocytes include Neutrophils, Eosinophils and Basophils. Agranulocytes include Monocytes and Lymphocytes. Each type of Leucocyte has its own function and is important for our body. Neutrophils and Monocytes bring about phagocytosis. Basophils are important during imflammation. Eosinophils are associated with allergic reactions. Lymphocytes are important for the immunity of the body.

Topic: Biology, Human Health and Diseases, NEET
A patient's urine shows the presence of proteins. This could be due to error in:

Options:
A Ultrafiltration
B Selective reabsorption
C Tubular secretion
D Micturition

The correct answer is:
Ultrafiltration

Solution:
The first step in urine formation is Ultrafiltration. This takes place in the glomerulus. The term means even the smallest particles are filtered in the bowman's capsule. All the substances are filtered except for the plasma proteins. Thus if the urine of the person shows presence of proteins, it is due to kidney damage or some error in the ultrafiltration process.

Topic: Biology, Excretory Products and their Elimination, NEET
A pea plant is heterozygous for a character and recessive homozygyous for another character. Both these characters are located on different chromosomes. Another pea plant of the same species is heterozygous for both the characters. If these plants are crossed, what proportion of their offsprings will be heterozygous only for one character?

Options:
A 25%
B 50%
C 75%
D 100%

The correct answer is:
50%

Solution:
Aabb is crossed with AaBb. Gametes produced by Aabb is Ab and ab. Gametes produced by AaBb are AB, Ab, aB and ab. The offsprings can be tabulated as follows:

AB	Ab	aB	ab
Ab	AABb	AAbb	AaBb	Aabb
ab	AaBb	Aabb	aaBb	aabb

The highlighted offsprings are heterozygous only for one character. Thus their proportion will be 4 out of 8 or 50%

Topic: Biology, Principles of Inheritance and Variation, NEET
A pendulum bob of mass 50 g is suspended from the ceiling of an elevator. The tension in the string if the elevator goes up with uniform velocity is approximately

Options:
A 0.30 N

B 0.40 N
C 0.42 N
D 0.50 N

The correct answer is:
0.50 N

Solution:
As elevator goes up with uniform velocity then acceleration a = 0
T = m g + a
T=mg=5Ã10-3Ã10
=0.5 N

Topic: Physics, Laws of Motion, NEET
A pendulum clock is 5 s fast at a temperature of 15 Â°C and 10 s slow at a temperature of 30 Â°C. At what temperature does it give the correct time? (take time interval = 24 hours)

Options:
A 18 °C

B 22 Â°C

C 20 Â°C

D 25 °C

The correct answer is:
20 Â°C

Solution:
Î t = 1 2 Î± Î T Ã t

â´ 5 = 1 2 Î± T - 1 5 Ã 8 6 4 0 0 .........(i)

And 1 0 = 1 2 Î± 3 0 - T Ã 8 6 4 0 0 ........(ii)

Dividing both equations,

12=T-1530-T

â 30-T=2T-30

â 3T=60â T = 20 Â°C

Topic: Physics, Thermal Properties of Matter, NEET
A pendulum clock which ticks 60 times in one minute on earth is placed on the moon where the acceleration due to gravity is only one-sixth of that on the earth. How many times the clock will tick over there in one minute?

Options:
A 12.25
B 24.5
C 2.45
D 0.245

The correct answer is:
24.5

Solution:
T ′ = 2 π lâ¡ / g / 6 = 6 T Hence, the clock will tick in one minute
= 6 0 / 6 = 2 4 . 5 times

Topic: Physics, Oscillations, NEET
A pendulum consisting of a small sphere of mass M suspended by an inextensible and massless string of length l is made to swing in a vertical plane. If the breaking strength of the string is 2 Mg, then the maximum angular amplitude of the displacement from the vertical can be

Options:
A 0°
B 30°
C 60°
D 90°

The correct answer is:
60°

Solution:
Tmax=mv2l+mg⇒2mg=mv2l+mg
⇒ v=gl   …1
Using energy conservation ΔKE=ΔPE
∵ 12mv2=mgh  ∴ h=v22g=l2   …2
∵cos⁡θ=l-hl=12  ∴θ=60°

Topic: Physics, Oscillations, NEET
A pendulum consisting of a small sphere of mass M suspended by an inextensible and massless string of length l is made to swing in a vertical plane. If the breaking strength of the string is 2Mg , then the maximum angular amplitude of the displacement from the vertical can be -

Options:
A 0°
B 30°
C 60°
D 90°

The correct answer is:
60°

Solution:
∴Tmax=mvA2l +mg
∴2mg=mvA2l+mg ⇒vA=gl
∴v2=vA2-2gl 1-cos⁡θ
∴0=gl-2gl 1-cos⁡θ
⇒cos⁡θ=1/2 ⇒θ=60°

Topic: Physics, Laws of Motion, NEET
A pendulum has maximum kinetic energy K1 . If its length is doubled keeping amplitude same then maximum kinetic energy becomes K2 . Then relation between K1 and K2 is:

Options:
A K2=2K1
B K1=2K2
C K2=K1
D K1=4K2

The correct answer is:
K2=2K1

Solution:
Maximum kinetic energy =12mω2A2
ω=gL
A=Lθ
KE=12 mgL×L2θ2
KE=12mgLθ2
If length is doubled
K2=12mg2Lθ2 [Here we are assuming angular amplitude is same]
K1K2=12mglθ212mg2Lθ2=12
K2=2K1

Topic: Physics, Oscillations, NEET
A pendulum has maximum kinetic energy K1 . If its length is doubled keeping amplitude same then maximum kinetic energy becomes K2 . Then the relation between K1 and K2 is:

Options:
A K2=2K1
B K1=2K2
C K2=K1
D K1=4K2

The correct answer is:
K2=2K1

Solution:
Maximum kinetic energy =12mω2A2
ω=gL
A=Lθ
KE=12 mgL×L2θ2
KE=12mgLθ2
If length is doubled
K2=12mg2Lθ2 [Here we are assuming angular amplitude is same]
K1K2=12mglθ212mg2Lθ2=12
K2=2K1

Topic: Physics, Oscillations, NEET