JEE Advanced 2021 Solutions | Physics Paper 2
#jeeadvanced2021 #jeephysics #paper2
0:00 Q1
One end of a horizontal uniform beam of weight 𝑊 and length 𝐿 is hinged on a
vertical wall at point O and its other end is supported by a light inextensible rope.
The other end of the rope is fixed at point Q, at a height 𝐿 above the hinge at point
O. A block of weight 𝛼𝑊 is attached at the point P of the beam, as shown in the
figure (not to scale). The rope can sustain a maximum tension of (2√2)𝑊. Which
of the following statement(s) is(are) correct?
6:46 Q2
A source, approaching with speed 𝑢 towards the open end of a stationary pipe of
length 𝐿, is emitting a sound of frequency 𝑓𝑠. The farther end of the pipe is closed.
The speed of sound in air is 𝑣 and 𝑓0 is the fundamental frequency of the pipe. For
which of the following combination(s) of 𝑢 and 𝑓𝑠, will the sound reaching the pipe
lead to a resonance?
10:58 Q3
For a prism of prism angle 𝜃 = 60°, the refractive indices of the left half and the
right half are, respectively, 𝑛1 and 𝑛2 (𝑛2 ≥ 𝑛1) as shown in the figure. The angle
of incidence 𝑖 is chosen such that the incident light rays will have minimum
deviation if 𝑛1 = 𝑛2 = 𝑛 = 1.5. For the case of unequal refractive indices, 𝑛1 = 𝑛
15:50 Q4
A physical quantity 𝑆⃗ is defined as 𝑆⃗ = (𝐸⃗⃗ × 𝐵⃗⃗)/𝜇0, where 𝐸⃗⃗ is electric field, 𝐵⃗⃗ is
magnetic field and 𝜇0 is the permeability of free space. The dimensions of 𝑆⃗ are the
same as the dimensions of which of the following quantity(ies) ?
18:42 Q5
A heavy nucleus 𝑁, at rest, undergoes fission 𝑁 → 𝑃 + 𝑄, where 𝑃 and 𝑄 are two
lighter nuclei. Let 𝛿 = 𝑀𝑁 − 𝑀𝑃 − 𝑀𝑄, where 𝑀𝑃, 𝑀𝑄 and 𝑀𝑁 are the masses of 𝑃,
𝑄 and 𝑁, respectively. 𝐸𝑃 and 𝐸𝑄 are the kinetic energies of 𝑃 and 𝑄, respectively.
22:23 Q6
Two concentric circular loops, one of radius 𝑅 and the other of radius 2𝑅, lie in the
xy-plane with the origin as their common center, as shown in the figure. The smaller
loop carries current 𝐼1 in the anti-clockwise direction and the larger loop carries
current 𝐼2 in the clockwise direction, with 𝐼2 2𝐼1. 𝐵⃗⃗(𝑥, 𝑦) denotes the magnetic
field at a point (𝑥, 𝑦) in the xy-plane. Which of the following statement(s) is(are)
correct?
30:04 Q7,8
A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass
test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has
a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc. Initially the
bottle is sealed at atmospheric pressure 𝑝0 = 105 Pa so that the volume of the
35:37 Q9,10
A pendulum consists of a bob of mass 𝑚 = 0.1 kg and a massless inextensible string
of length 𝐿 = 1.0 m. It is suspended from a fixed point at height 𝐻 = 0.9 m above
a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor
at rest vertically below the point of suspension. A horizontal impulse
𝑃 = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some
distance, the string becomes taut and the bob lifts off the floor. The magnitude of
the angular momentum of the pendulum about the point of suspension just before
the bob lifts off is 𝐽 kg-m2/s. The kinetic energy of the pendulum just after the liftoff is 𝐾 Joules.
38:37 Q11,12
In a circuit, a metal filament lamp is connected in series with a capacitor of
capacitance C 𝜇𝐹 across a 200 V, 50 Hz supply. The power consumed by the lamp
is 500 W while the voltage drop across it is 100 V. Assume that there is no inductive
40:43 Q13,14
A special metal 𝑆 conducts electricity without any resistance. A closed wire loop,
made of 𝑆, does not allow any change in flux through itself by inducing a suitable
current to generate a compensating flux. The induced current in the loop cannot
decay due to its zero resistance. This current gives rise to a magnetic moment
which in turn repels the source of magnetic field or flux. Consider such a loop, of
44:15 Q15,16
A thermally insulating cylinder has a thermally insulating and frictionless
movable partition in the middle, as shown in the figure below. On each side of the
partition, there is one mole of an ideal gas, with specific heat at constant volume,
𝐶𝑉 = 2𝑅. Here, 𝑅 is the gas constant. Initially, each side has a volume 𝑉0 and
temperature 𝑇0. The left side has an electric heater, which is turned on at very low
power to transfer heat 𝑄
48:48 Q17
In order to measure the internal resistance 𝑟1 of a cell of emf 𝐸, a meter bridge of
wire resistance 𝑅0 = 50 Ω, a resistance 𝑅0/2, another cell of emf 𝐸/2 (internal
resistance 𝑟) and a galvanometer G are used in a circuit
51:02 Q18
The distance between two stars of masses 3𝑀𝑆 and 6𝑀𝑆 is 9𝑅. Here 𝑅 is the mean
distance between the centers of the Earth and the Sun, and 𝑀𝑆 is the mass of the
Sun. The two stars orbit around their common center of mass in circular orbits with
period 𝑛𝑇
53:12 Q19
In a photoemission experiment, the maximum kinetic energies of photoelectrons
from metals 𝑃, 𝑄 and 𝑅 are 𝐸𝑃, 𝐸𝑄 and 𝐸𝑅, respectively, and they are related by
𝐸𝑃 = 2𝐸𝑄 = 2𝐸𝑅