Physics || JEE Main previous year questions with Solutions

Q 1 :
If a rubber ball falls from a height $h$ and rebounds up to the height of $h / 2$ . The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are [2024]

$40 %, \sqrt{2 g h}$
$50 %, \sqrt{\frac{g h}{2}}$
$50 %, \sqrt{2 g h}$
$50 %, \sqrt{g h}$

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(3)

Velocity just before collision = $\sqrt{2 g h}$

Velocity just after collision = $\sqrt{2 g (\frac{h}{2})}$

$∴$ $∆ K E = \frac{1}{2} m (2 g h) - \frac{1}{2} m g h = \frac{1}{2} m g h$

$∴$ % loss in energy $\frac{∆ K E}{K E_{i}} \times 100$

$\Rightarrow \frac{∆ K E}{K E_{i}} \times 100 = \frac{\frac{1}{2} m g h}{\frac{1}{2} m g 2 h} \times 100 = 50 %$

Q 2 :
A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m. The impulse of force imparted by the ground to the body is given by (given $g = 9.8$ $m / s^{2}$ ) [2024]

4.32 kg ${ms}^{- 1}$
43.2 kg ${ms}^{- 1}$
23.9 kg ${ms}^{- 1}$
2.39 kg ${ms}^{- 1}$

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(4)

$m = 100 g = 0.1 kg, h_{1} = 10 m, h_{2} = 5 m$

$u = \sqrt{2 g h_{1}} = \sqrt{2 \times 98} m/s$

$v = \sqrt{2 g h_{2}} = \sqrt{98} m/s$

Impulse $= Δ \vec{P} = {\vec{P}}_{f} - {\vec{P}}_{i}$

$= 0.1 [\sqrt{98} + \sqrt{2 \times 98}]$

$\approx 2.39 kg m/s$

Q 3 :
A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass $10^{- 2}$ kg moving with a speed of $2 \times 10^{2}$ ${ms}^{- 1}$ . The bullet gets embedded into the bob. The height to which the bob rises before swinging back is (use $g = 10$ $m / s^{2}$ ) [2024]

0.30 m
0.20 m
0.35 m
0.40 m

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(2)

$P_{i} = P_{f} \Rightarrow m u = (M + m) V$

$m u = (M + m) V$

$10^{- 2} \times 2 \times 10^{2} ≅ 1 \times V \Rightarrow V ≅ 2 m/s$

Q 4 :
As shown below, bob A of a pendulum having massless string of length 'R' is released from 60° to the vertical. It hits another bob B of half the mass that is at rest on a friction less table in the centre. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (Take g as acceleration due to gravity) [2025]

$\frac{1}{3} \sqrt{R g}$
$\sqrt{R g}$
$\frac{4}{3} \sqrt{R g}$
$\frac{2}{3} \sqrt{R g}$

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(1)

Velocity of a just before hitting:

$u = \sqrt{2 g \frac{R}{2}} = \sqrt{g R}$

Just after collision, let velocity of A and B are $v_{1}$ and $v_{2}$ respectively

By COM: $m u = m v_{1} + \frac{m}{2} v_{2}$

$2 v_{1} + v_{2} = 2 u$ ... (i)

$e = 1 = \frac{v_{2} - v_{1}}{u}$

$\Rightarrow v_{2} - v_{1} = u$ ... (ii)

From (i) and (ii)

$\Rightarrow 3 v_{1} = u \Rightarrow v_{1} = \frac{u}{3} = \frac{1}{3} \sqrt{g R}$

Q 5 :
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) :

Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities $V_{A}$ = 5 m/s, $V_{B}$ = 2 m/s, $V_{C}$ = 4 m/s. If we wait sufficiently long for elastic collision to happen, then $V_{A}$ = 4 m/s, $V_{B}$ = 2 m/s, $V_{C}$ = 5 m/s will be the final velocities.

Reason (R) : In an elastic collision between identical masses, two objects exchange their velocities.

In the light of the above statements, choose the correct answer from the options given below: [2025]

Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
(A) is true but (R) is false
Both (A) and (R) are true and (R) is the correct explanation of (A)
(A) is false but (R) is true

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(4)

In elastic collision for same mass, velocities interchange for

Final velocity

$V_{A}$ = 2 m/s

$V_{B}$ = 4 m/s

$V_{C}$ = 5 m/s

Topic Question Set

Q 1 :
If a rubber ball falls from a height $h$ and rebounds up to the height of $h / 2$ . The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are [2024]

Q 2 :
A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m. The impulse of force imparted by the ground to the body is given by (given $g = 9.8$ $m / s^{2}$ ) [2024]

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Topic Question Set

Q 1 : If a rubber ball falls from a height h and rebounds up to the height of h/2. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are [2024]

Q 2 : A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m. The impulse of force imparted by the ground to the body is given by (given g=9.8 m/s2) [2024]

Q 3 : A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass 10-2 kg moving with a speed of 2×102 ms-1. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is (use g=10 m/s2) [2024]

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Q 1 :
If a rubber ball falls from a height $h$ and rebounds up to the height of $h / 2$ . The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are [2024]

Q 2 :
A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m. The impulse of force imparted by the ground to the body is given by (given $g = 9.8$ $m / s^{2}$ ) [2024]