Grass-G/jee-main-questions huggingface dataset:
Subject: Physics — Vector — Angle between vectors
Difficulty: Moderate

Question: There are two vectors
$\overset{\rightarrow}{OA}\&\overset{\rightarrow}{OB}$. Vector
$\overset{\rightarrow}{OA}$ is inxy plane and of magnitude 5 units and
vector $\overset{\rightarrow}{OB}$ isx-z plane and of magnitude
$\sqrt{2}$units as shown. Theangle between the vectors
$\overset{\rightarrow}{OA}\&\overset{\rightarrow}{OB}$is$\theta = \cos^{- 1}(\frac{3}{n\sqrt{2}})$.
Find n.



Solution:
$\overset{\rightarrow}{OA} = 5cos53^{\circ}\overset{\hat{}}{i} + 5sin53^{\circ}\overset{\hat{}}{j} = 3\overset{\hat{}}{i} + 4\overset{\hat{}}{j}$
$\overset{\rightarrow}{OB} = \sqrt{2}cos45^{\circ}\overset{\hat{}}{i} + \sqrt{2}sin45^{\circ}\overset{\hat{}}{k} = 1\overset{\hat{}}{i} + 1\overset{\hat{}}{k}$
$cos\theta = \frac{\overset{\rightarrow}{OA} \cdot \overset{\rightarrow}{OB}}{|\overset{\rightarrow}{OA}||\overset{\rightarrow}{OB}|} = \frac{3 + 0}{5 \cdot \sqrt{2}} = \frac{3}{5\sqrt{2}}$
$\Rightarrow \theta = \cos^{- 1}(\frac{3}{5\sqrt{2}})$
Subject: Physics — Center of mass — Motion of center of mass
Difficulty: Tough

Question: An object A is dropped from rest from the top of a 30 m high
building and at the same moment another object B is projected vertically
upwards with an initial speed of 15 m/s from the base of the building.
Mass of the object A is 2 kg while mass of the object B is 4kg. The
maximum height above the ground level attained by the centre of mass of
the A and B system is (take$g = 10m/s^{2}$)

1) 15 m
2) 25 m
3) 30 m
4) 35 m

Correct option: 1

Solution:
Using
$\frac{m_{1}{\overset{\rightarrow}{x}}_{1} + m_{2}{\overset{\rightarrow}{x}}_{2}}{m_{1} + m_{2}} = X_{cm}$
By putting values $X_{cm} = 10\ m$from base.
[IMAGE] Initial velocity of
COM$\Rightarrow \frac{m_{1}v_{1} + m_{2}v_{2}}{m_{1} + m_{2}} = 10m/supward$
Also, acceleration of COM is g thus using
$v^{2} = u^{2} + 2$as for COM
$0 = 10^{2} + 2 \times ( - 10) \times h_{\max}$
$h_{\max} = 5m$from the initial position of COM
Hence total height from base$= 10 + 5m = 15m$
Subject: Physics — Electronic devices — Gates
Difficulty: Moderate

Question: In the given circuit, value of Y is:
 ifjiFk

1) Toggles between 0 and 1 0
2) 0
3) will not execute ifjiFk dk;kZ fuor ugha gksxk
4) 1

Correct option: 2

Solution:
Subject: Physics — Electrostatics — Electric field by uniformly charged sphere
Difficulty: Moderate

Question: Consider a sphere of radius R which carries a uniform charge
density$\rho$. If a sphere of radius$\frac{R}{2}$iscarved out of it, as
shown, the
ratio$\left| \frac{{\overset{\rightarrow}{E}}_{A}}{{\overset{\rightarrow}{E}}_{B}} \right|$
of magnitude of electric field of magnitude of electric field
${\overset{\rightarrow}{E}}_{A}\ $and ${\overset{\rightarrow}{E}}_{B}$,
respectively, atpoints A and B due to the remaining portion is

1) $\frac{9}{17}$
2) $\frac{21}{34}$
3) $\frac{17}{54}$
4) $\frac{18}{54}$

Correct option: 1

Solution:
For a solid sphere
$E = \frac{\rho r}{3\varepsilon_{0}}$
$E_{A} = \frac{- \rho R}{2\left( 3\varepsilon_{0} \right)}$
$\left| E_{A} \right| = \frac{\rho R}{6\varepsilon_{0}}$
Electric field at point B = E_B = E_1A + E_2A
E_1A = Electric Field Due to solid sphere of radius R at point
$B = \frac{\rho R}{3\varepsilon_{0}}$
E_2A = Electric Field Due to solid sphere of radius R/2 (which having
charge density -$\rho$)$= - \frac{\rho R}{54\varepsilon_{0}}$
Subject: Physics — Rigid Body Dynamics — Kinetic energy in combined motion
Difficulty: Moderate

Question: A uniform sphere of mass 500 g rolls without slipping on a plane
horizontal surface with its centre moving at a speed
of[IMAGE]. Its kinetic energy is


Correct option: 1

Solution:
K.E. of the sphere = Translational K.E + Rotational K.E.
[IMAGE] K = Radius of gyration
Subject: Physics — Mechanical Properties of Fluids — Buoyant force
Difficulty: Moderate

Question: A small ball of mass m is released from rest from a height h
above the liquid surface. The density of ball is $\frac{\rho}{3}$:
(assume no splash)

1) If $h \geq H$, then the ball will be able to enter the liquid of
higher density
2) If $h \geq \frac{7H}{2}$, then the ball will be able to strike the
bottom of the vessel
3) If h = 2H, then the ball will cross the interface of two liquids
with kinetic energy = mgH and If h = 0 then ball will float on the
surface.
4) All of the above

Correct option: 4

Solution:
$mg\left( h + \frac{H}{2} \right) = \lbrack v\rho g\rbrack\frac{H}{2}$
h= H
$mg\left( h + \frac{H}{2} + \frac{H}{2} \right) = \lbrack v\rho g\rbrack\frac{H}{2} + \lbrack v2\rho g\rbrack\frac{H}{2}$
$mg\left( \frac{5H}{2} \right) - \frac{3}{2}mgH = K.E$
K.E. = mgH.
Subject: Physics — Newton's Laws of Motion — Friction
Difficulty: Moderate

Question: For the situation shown in figure below, there is no friction
between pulley and string. For which of the following values of mass of
block A, the system will stay at rest $(g = 10m/s^{2})$

1) 4 Kg
2) 8 Kg
3) 16 Kg
4) 30 Kg

Correct option: 4

Solution:
Tension in string =100 N in equilibrium F.B.D. of A
$F_{s} = 80 \leq \mu N$
$80 \leq \frac{1}{2}(mg - 60)$
$mg \geq 220$
$m \geq 22$
Subject: Physics — Dual Nature of Matter — Einstein's photoelectric equation
Difficulty: Moderate

Question: When a metallic surface is illuminated with monochromatic light
of wavelength [IMAGE] the stopping potential is
[IMAGE] When the same surface is illuminated with light
of wavelength [IMAGE] the stopping potential is
[IMAGE] Then the work function of the metallic surface
is $\frac{hc}{x\lambda},$ where value of x


Answer: 6

Solution:
Subject: Physics — Error analysis — 
Difficulty: Easy

Question: The pressure on a square plate is measured by measuring the
force on the plate and the lengthof the sides of plate. If the maximum
error in themeasurement of force and length are respectively 4 and 2 then what is the maximum percentage error in themeasurement of pressure?

1) 1
2) 2
3) 6
4) 8

Correct option: 4

Solution:
$P = \frac{F}{A};\ \ \lbrack P\rbrack = \left\lbrack \frac{F}{A} \right\rbrack = \left\lbrack \frac{{MLT}^{- 2}}{L^{2}} \right\rbrack = \left\lbrack {ML}^{- 1}T^{- 2} \right\rbrack$
Subject: Physics — Modern physics — Balmer spectral series
Difficulty: Moderate

Question: The first member of the Balmer series of hydrogen atom has a
wavelength of The wavelength of the second member of the Balmer
series (in nm) is 81n. Find n.


Answer: 6

Solution:
$\frac{1}{\lambda} = RZ^{2}(\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$
$\frac{1}{\lambda_{1}} = R(1)^{2}(\frac{1}{2^{2}} - \frac{1}{3^{2}}) = \frac{5R}{36}$
$\frac{1}{\lambda_{2}} = R(1)^{2}(\frac{1}{2^{2}} - \frac{1}{4^{2}}) = \frac{3R}{16}$
$\frac{\lambda_{2}}{\lambda_{1}} = \frac{20}{27}$
$\lambda_{2} = \frac{20}{27} \times 6561A = 4860Å$
$= 486nm$
Subject: Physics — Thermodynamics — V-T diagram
Difficulty: Moderate

Question: V - T diagram for a process of a given mass of ideal gas is as
shown in the figure. During the process pressure of gas.

1) First increases then decreases
2) Continuously decreases
3) Continuously increases
4) First decreases then increases.

Correct option: 2

Solution:
$V = KT + C$
$P = \frac{nRT}{V}$
$\Rightarrow P = \frac{nRT}{KT + C}$
$\frac{dP}{dT} = \frac{nRC}{(KT + C)^{2}}$
As C < 0 by diagram
$\Rightarrow \frac{dP}{dT} < 0$ for all T
$\Rightarrow$ P continuously decreases
Subject: Physics — Electrostatics — Electric field by uniformly charged sphere
Difficulty: Moderate

Question: Consider a sphere of radius R which carries a uniform charge
density$\rho$. If a sphere of radius$\frac{R}{2}$iscarved out of it, as
shown, the
ratio$\left| \frac{{\overset{\rightarrow}{E}}_{A}}{{\overset{\rightarrow}{E}}_{B}} \right|$
of magnitude of electric field of magnitude of electric field
${\overset{\rightarrow}{E}}_{A}$ and ${\overset{\rightarrow}{E}}_{B}$,
respectively, atpoints A and B due to the remaining portion is

1) $\frac{18}{34}$
2) $\frac{21}{34}$
3) $\frac{17}{54}$
4) $\frac{18}{54}$

Correct option: 1

Solution:
For a solid sphere
$E = \frac{\rho r}{3\varepsilon_{0}}$
$E_{A} = \frac{- \rho R}{2\left( 3\varepsilon_{0} \right)}$
$\left| E_{A} \right| = \frac{\rho R}{6\varepsilon_{0}}$
Electric field at point B = E_B = E_1A + E_2A
E_1A = Electric Field Due to solid sphere of radius R at point
$B = \frac{\rho R}{3\varepsilon_{0}}$
E_2A = Electric Field Due to solid sphere of radius R/2 (which having
charge density -$\rho$)
$= - \frac{{KQ}^{'} \times 4}{{OR}^{2}} = - \frac{\rho R}{54\varepsilon_{0}}$
Subject: Physics — Rigid Body Dynamics — Conservation of mechanical energy
Difficulty: Moderate

Question: A uniformly thick wheel with moment of inertial I and radius R is
free to rotate about its centre of mass (see figure). A massless string
is wrapped over its rim and two blocks of masses [IMAGE] and [IMAGE] are attached to the ends of the string. The
system is released from rest. The angular speed of the wheel
when[IMAGE] descents by a distance his


Correct option: 2

Solution:
Subject: Physics —  — 
Difficulty: Easy

Question: The following figure depicts a wave travelling in a medium.
Which pair of particles are in phase.

1) A and G
2) B and F
3) C and E
4) B and F

Correct option: 1

Solution:
Point is moving down though
they are at the same distance from equilibrium position at the instant
shown. Therefore B and F are not in phase.
By same argument, A and G are in phase.
TOPIC:Waves in a string
SUB TOPIC: Particles in phase
Subject: Physics — Moving charges and — Magnetic field due to current carrying conducting
Difficulty: Moderate

Question: The radius of a coil of wire with 21 turns is 0.22 m, and i_2
current flows clockwise in the coil as shown. A long straight wire
carrying a current is toward the left is located 0.05 m from the edge of
the coil. The magnetic field at the centre of the coil is zero tesla.
The ratio $\frac{i_{1}}{4i_{2}}$ is (Use$\pi = 22/7$)


Answer: 20.25

Solution:
$\frac{\mu_{0} \cdot i_{1}}{2\pi(d + r)} = \frac{N \times \mu_{0}i_{2}}{2r}$
$\Rightarrow N = \frac{i_{1}}{i_{2}} \cdot \frac{r}{\pi(d + r)}$
$\frac{i_{1}}{i_{2}} = 81$
Subject: Physics — Centre of Mass — Conservation of momentum
Difficulty: Moderate

Question: A railway flat car has an artillery gun installed on it and
contains shells for fring The combined system excluding shell has a mass
M and moves with a velocity $v_{0}$. The barrel of the gun makes an
angle $\alpha$ with the horizontal. A shell of mass m leaves the barrel
at a speed relative to initial state of barrel in the forward
direction. The speed of the flat car so that it may stop after the
firing is: (neglect frinstion)

1) $\ \frac{mu}{M + m}$
2) $(\frac{Mu}{M + m})cos\alpha$
3) $(\frac{mu}{M})cos\alpha$
4) $\ (M + m)ucos\alpha$

Correct option: 3

Solution:
u - velocity of shell with respect to gun.
In horizontal direction ${\overset{\rightarrow}{F}}_{ext} = 0$, so
centre of mass move with constant velocity in horizontal plane.
$(M + m)v_{0} = m(v_{0} + ucos\alpha)$
$V_{0} = \frac{mucos\alpha}{M}$
Subject: Physics — Sound wave — Doppler effect
Difficulty: Moderate

Question: Sound of frequency 1000 Hz from a stationary source is reflected
from an object approaching the source at 30 m/s, back to a stationary
observer located at the source. The speed of sound in air is 330 m/s.
The frequency of the sound heard by the observer is

1) 1200Hz
2) 1200Hz
3) 1090Hz
4) 1100Hz

Correct option: 1

Solution:
Subject: Physics — Rotational motion — Rolling with sliding
Difficulty: Tough

Question: A solid sphere of mass m and radius r is gently placed on a
conveyer belt moving with constant velocityV. If the coefficient of
friction between the belt and sphere is$\frac{2}{7}$, the distance
travelled by the centre of the sphere before it starts pure rolling is.

1) $\frac{v^{2}}{7g}$
2) $\frac{2V^{2}}{49g}$
3) $\frac{2V^{2}}{5g}$
4) $\frac{2V^{2}}{7g}$

Correct option: 1

Solution:
Initial situation w.r.t. the conveyer belt:
$\mu mgR = \frac{2}{5}{mR}^{2} \cdot \alpha$ $\Rightarrow$
$\alpha = \frac{5}{7} \cdot \frac{g}{R}$
At pure rolling:
$v^{'} = v - (\mu g)t$and $\omega^{'} = 0 + \left( \frac{5}{7} \cdot \frac{g}{R} \right)t$
(Since at pure rolling)
$\Rightarrow$ $v - \mu gt = \frac{5}{7} \cdot g \cdot t$
$\Rightarrow$ $t = \frac{v}{g}\left( \because\mu = \frac{2}{7} \right)$
For centre of the sphere:$S = v\left( \frac{v}{g} \right) - \frac{1}{2} \cdot \left( \frac{2}{7} \cdot g \right)\left( \frac{v^{2}}{g^{2}} \right)$
$S = \frac{v^{2}}{g} - \frac{v^{2}}{7g}$ (w.r.t. belt)
In this time, the belt with speed will move a distance
of$s_{b} = vt = v\left( \frac{v}{g} \right) = \frac{v^{2}}{g}$
[IMAGE] Distance travelled w.r.t. ground will be:$S_{g} = \left| S - S_{b} \right| = \left| \left( \frac{v^{2}}{g} - \frac{v^{2}}{7g} \right) - \left( \frac{v^{2}}{g} \right) \right| = \frac{v^{2}}{7g}$
Subject: Physics — Mechanical Properties of Fluids — Buoyancy
Difficulty: Moderate

Question: A leak proof cylinder of length 1m, made of a metal which has
very low coefficient of expansion is floating vertically in water at 0ºC
such that its height above the water surface is 20 cm. When the
temperature of water is increased to 4ºC, the height of the cylinder
above the water surface becomes 21 cm. The density of water at T = 4ºC,
relative to the density at T = 0ºC is close to:,d yhd iwQ 1m yEck csyukdkj crZu,d,slh cuk gqvk gS ftldk
4ºC rd c<+k rks blds ckgj jgus okys Hkkx

1) 1.03
2) 1.04
3) 1.26
4) 1.01

Correct option: 4

Solution:
Subject: Physics — Wave Optics — YDSE
Difficulty: Moderate

Question: In a double-slit experiment, at a certain point on the screen
the path difference between the two interfering waves is
$\frac{1}{8}$thof a wavelength. The ratio of the intensity of light at
that point to that at the centre of a bright fringe is

1) 0.568
2) 0.760
3) 0.853
4) 0.672

Correct option: 3

Solution:
$I = I_{0}\cos^{2}(\frac{\Delta\phi}{2})$
$\frac{I}{I_{0}} = \cos^{2}\lbrack\frac{\frac{2\pi}{\lambda} \times \Delta x}{2}\rbrack = \cos^{2}(\frac{\pi}{8})$;
$\frac{I}{I_{0}} = 0.853$
Subject: Physics — Magnetism — Coercivity
Difficulty: Moderate

Question: The coercivity of a small magnet where the ferromagnet gets
demagnetized is 3 × 10^3 Am^-1. The current required to be passed in
a solenoid of length 10 cm and number of turns 100, so that the magnet
gets demagnetized when inside the solenoid, is

1) 30 mA
2) 60 mA
3) 3 A
4) 6 A

Correct option: 3

Solution:
For solenoid
$\frac{B}{\mu_{0}} = H$ or $B = \mu_{0}nI$
$H = nI$
$\Rightarrow 3 \times 10^{3} = \frac{100}{0.1} \times I$
Ι = 3A
Subject: Physics — Thermodynamics — Isobaric process
Difficulty: tough

Question: Figure shows the variation of internal energy "U" with the
density "$\rho$ " of one mole of ideal diatomic gas. Process BA is a
part of rectangular hyperbola. If the work done by gas in the process BA
is 7n joules. Find n ?
 &ijek.kqd xSl ds,d fLFkfrt 
 ?kuRo [IMAGE]


Answer: 2

Solution:
XY = constant constant (isobaric process) fu;rkad¼lenkch
Subject: Physics — Thermodynamics — V-T diagram
Difficulty: Moderate

Question: V-T diagram for a process of a given mass of ideal gas is as
shown in the figure. During the process pressure of gas.
çfØ;k

1) first increases then decreases
2) continuously decreases
3) continuously increases
4) first decreases then increases.

Correct option: 2

Solution:
[IMAGE] As C<0 by diagram
tSlk fd fp= }kjkC<0
[IMAGE] P continuously decreasesyxkrkj ?kVrk gSA
Subject: Physics —  — 

Question: Which one of the following choices is closest to the order of
the angular momentum of the Earth (expressed in base MKS units)
associated with its rotation about its axis ?

1) 1038
2) 1034
3) 1030
4) 1022

Correct option: 2

Solution:
m = 6 × 1024 kg
R = 6.4 × 106 m
I = [IMAGE] mR2
L = Iω = [IMAGE] × 6 × 1024 × (6.4 × 106)2
×[IMAGE] = [IMAGE] × 0.39 × 1034
Subject: Physics —  — 
Difficulty: Moderate

Question: A non-viscous fluid of density [IMAGE] is flowing
in a tube as shown in figure. Area of section

1) is double that of
section
2) . Centre of mass of section
3) Work done by gravitational force per unit volume from
section
4) Work done by elastic forces (pressure) per unit volume from
section

Correct option: 2

Solution:
Applying Bernoulli is equation from section-(1) and (2)
Solving we get,
[IMAGE] (3) Work done by gravitation force per unit volume = negative of the
increase in gravitational potential energy per unit volume =
$- (\rho gh)$
(4) Work done by elastic force per unit volume = decrease in
pressure = [IMAGE] = $2\rho gh$
TOPIC:Fluid dynamics
SUB TOPIC:Bernoulli's theorem
Subject: Physics — Mechanical properties of solid — Young's modulus
Difficulty: Moderate

Question: The stress versus strain graphs for wires of two materials A and
B are as shown in the figure. If $Y_{A}$ and $Y_{B}$ are the Young's
modulii of the materials, then
izfrcy rFkk fod`fr xzkQksa dks nks inkFkksZ A rFkk B

1) $Y_{B} = 2Y_{A}$
2) $Y_{A} = Y_{B}$
3) $Y_{B} = 3Y_{A}$
4) $Y_{A} = 3Y_{B}$

Correct option: 4

Solution:
$\frac{\ Stress\ }{\ Strain\ } = Y = \ slope\ of\ graph\ $
Subject: Physics — Current Electricity — KVL
Difficulty: Moderate

Question: The current (in A) flowing through battery is2n. Find the value


Answer: 1

Solution:
The diode D_1is reverse-biased and acts as an open switch as
shown in Fig. So, there is no currentthrough D_1and the
However, D_2is forward biased and acts like a short-current or closed
switch. The current drawn isI = 12/(2 + 4) = 2A.
Subject: Physics — Magnetics — Motion of charged particle in uniform electric field
Difficulty: Easy

Question: A particle of mass m and charge q is released from rest in a
uniform electric field. If there is no other force on the particle, the
dependence of its speed v on the distance x travelled by it is correctly
given by (graphs are schematic and not drawn to scale)


Correct option: 2

Solution:
$V^{2} = \frac{2qE}{m}x$
$$
Subject: Physics — Magnetism — Magnetic moment
Difficulty: Easy

Question: What would be the magnetic moment of given current distribution

1) $\frac{3\pi{IR}^{2}}{4} \odot$
2) $\frac{3\pi{IR}^{2}}{4} \otimes$
3) $\frac{3\pi{IR}^{2}}{2} \odot$
4) $\frac{3\pi{IR}^{2}}{2} \otimes$

Correct option: 2

Solution:
$M = \frac{I}{4}\left\{ \pi(2R)^{2} - \pi(R)^{2} \right\}$ =
$\frac{3\pi{IR}^{2}}{4}$
Subject: Physics — Mechanical Properties of Fluids — Bernoulli's equation
Difficulty: Moderate

Question: Water flows in a horizontal tube (see figure). The pressure of
water changes by [IMAGE] between Aand B where the area of
cross section are [IMAGE] respectively. Find the rate of
flow ofwater through the tube.
(density of water [IMAGE],d {kSfrt uyh esa ikuh cg jgk gS ¼fp= ns[ksa½A bl uyh esa A ls B ds
chp ikuh ds ncko vUrj
dh vuqçLFk dkV A uyh esa ikuh


Correct option: 1

Solution:
Using equation of continuity lehdj.k Using Bernoullies equation cjuksyh lehdj.k
Subject: Physics —  — 
Difficulty: Moderate

Question: A particle is revolving in a circle of radius r and centre at
'O' with uniform angular velocity [IMAGE]. Let angular
velocity at A about O, B, and C is[IMAGE],
the correct option

4) None of these.

Correct option: 3

Solution:
[IMAGE] TOPIC:Rigid body dynamics
SUB TOPIC: Angular velocity
Subject: Physics — Rigid Body Dynamics — Conservation of angular momentum
Difficulty: Moderate

Question: Two men of equal masses stand at opposite ends of the diameter of
a turntable disc of a certain mass, moving with some angular velocity.
The two men start moving towards the center of the turntable atequal
rates. Then choose the correct option

1) Kinetic energy of the system will increase.
2) Kinetic energy of system will decrease.
3) Angular momentum of the system will increase.
4) Angular momentum of the system will decrease.

Correct option: 1

Solution:
$I_{1}\omega_{1} = I_{2}\omega_{2}$
Since, men move towards middle of turn table Ι decreases hence
$\omega_{2}$increases.
$\therefore$ $KE = \frac{L^{2}}{2I};L =$constant and I decreases so KE
increases
Subject: Physics — Thermodynamics — Ideal gas equation
Difficulty: Moderate

Question: The expansion of unit mass of an ideal gas atconstant pressure
is show in the diagram. Here

1) a= volume,b=K (Kelvine) temperature c
2) a= volume,b= ºC temperature
3) a= ºC temperature, b= volume
4) a=K temperature, b= volume

Correct option: 3

Solution:
$PV = nRT(K)$
$V = \frac{nR}{P}T(K)$
$V = \frac{nR}{P}\lbrack T_{c}^{o} + 273\rbrack$
$V = \frac{nR}{P}T_{c}^{o} + 273\frac{nR}{P}$
$\Rightarrow T_{c}^{o} = \frac{P}{nR}V - 273$
$y = mx - c$
Subject: Physics —  — 
Difficulty: Tough

Question: A observer standing in a cart which has acceleration g on
horizontal road is observing vertical circular motion of a pendulum. One
end of the pendulum string is at rest at O with respect to the cart.
Choose the possible position of minimum speed for the pendulum with
respect to cart during complete vertical circular motion from the figure
given below

1) 1
2) 2
3) 3
4) 4
 g 
 O

Correct option: 3

Solution:
Opposite to geffect.
TOPIC: CIRCULAR MOTION
SUB TOPIC: DYNAMICS
Subject: Physics — Isobaric process — Thermodynamics
Difficulty: Moderate

Question: If N Joules of heat is to be transferred to nitrogen in the
isobaric heating process for that gas to perform the work A =2.0 J then
the value of N is
[IMAGE] xSl dks nh x;h dk eku N twy gksrk gS] rks
N


Answer: 7

Solution:
W = 2J
Subject: Physics — Mechanical Properties of Fluids — Bernoulli's equation
Difficulty: Moderate

Question: Two liquids of densities $\rho_{1}\ $and
$\rho_{2}\left( \rho_{2} = 2\rho_{1} \right)$ are filled up behind a
square wall of side 10 m as shown in figure. Each liquid has a height of
5 m. The ratio of the forces due to these liquids exerted on upper part
MN to that at the lower part NO is (Assume that the liquids are not
mixing)

1) $\frac{1}{2}$
2) $\frac{1}{3}$
3) $\frac{1}{4}$
4) $\frac{2}{3}$

Correct option: 3

Solution:
Subject: Physics — Motion in 1D — Motion under gravity
Difficulty: Tough

Question: A balloon rises from rest on the ground with constant
acceleration $\left( \frac{g}{8} \right)$. A stone is dropped when the
balloon has risen to a height H metre. Then, the time taken by the stone
to reach the ground is: (t=0 is the moment when stone is dropped)

1) $\frac{3}{2}\sqrt{\frac{H}{g}}$
2) $\frac{1}{2}\sqrt{\frac{H}{g}}$
3) $\sqrt{\frac{H}{g}}$
4) $2\sqrt{\frac{H}{g}}$

Correct option: 4

Solution:
$v^{2} = 0 + 2 \times \frac{g}{8} \times H \Rightarrow v = \frac{\sqrt{gH}}{2}$
$- H = \frac{\sqrt{gH}}{2}t - \frac{1}{2}{gt}^{2} \Rightarrow t = \frac{\sqrt{gH} \pm 3\sqrt{gH}}{2g}$
$\Rightarrow t = 2\sqrt{\frac{H}{g}}$ (taking positive value)
Subject: Physics — Mechanical Properties of Fluids — Fluid in motion
Difficulty: Moderate

Question: An open rectangular tank of height 3m and length and width
respectively 5m and 3m contains water up to height 2m. It is accelerated
horizontally along the longer side. Find the acceleration of the tank so
that 10 of water spills


Correct option: 2

Solution:
$\ \Rightarrow y = \frac{12}{5}$
$\ tan\theta = \frac{y}{5} = \frac{a}{g}$
$\ \Rightarrow a = \frac{24}{5}$
Subject: Physics — Centre of Mass — Velocity of center of mass
Difficulty: Moderate

Question: Two blocks of mass 10 kg and 4 kg are connected by a spring of
negligible mass and are placed on a frictionless horizontal surface. An
impulse gives a speed of $14{ms}^{- 1}$ to the heavier block in the
direction of the lighter block. Then, the velocity of the centre of mass
is

1) $30\ {ms}^{- 1}$
2) $20\ {ms}^{- 1}$
3) $10\ {ms}^{- 1}$
4) $5\ {ms}^{- 1}$

Correct option: 3

Solution:
$= \frac{10 \times 14 + 4 \times 0}{10 + 4} = 10m/s$.