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

Q 6 :

As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball Q after collision will be (g = 10 $m / s^{2}$ ) [2023]

[IMAGE 43]

0
0.25 m/s
2 m/s
4 m/s

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(3)

The velocities will be interchanged after collision. Speed of P just before collision $= \sqrt{2 g h}$

$= \sqrt{2 \times 10 \times 0.2}$

$= 2 m/s$

Q 7 :

A ball of mass 200 g rests on a vertical post of height 20 m. A bullet of mass 10 g, travelling in horizontal direction, hits the centre of the ball. After collision both travel independently. The ball hits the ground at a distance 30 m and the bullet at a distance of 120 m from the foot of the post. The value of initial velocity of the bullet will be (if g = 10 $m / s^{2}$ ) [2023]

120 m/s
60 m/s
400 m/s
360 m/s

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(4)

[IMAGE 44]

$v_{1} = \frac{30}{\sqrt{\frac{2 h}{g}}}, v_{2} = \frac{120}{\sqrt{\frac{2 h}{g}}}$

$(0.01) u = (0.2) \frac{30 \sqrt{g}}{\sqrt{2 h}} + (0.01) \frac{120 \sqrt{g}}{\sqrt{2 h}}$

$u = 300 + 60 = 360 {ms}^{- 1}$

Q 8 :

A bullet of mass 0.1 kg moving horizontally with speed 400 ${ms}^{- 1}$ hits a wooden block of mass 3.9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and the surface is ______.(Given g = 10 $m / s^{2}$ ) [2023]

0.25
0.50
0.90
0.65

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(1)

[IMAGE 45]

$P_{i} = P_{f} (collision)$

$\Rightarrow (0.1) (400) = (0.1 + 3.9) v$

$\Rightarrow v = \frac{0.1 \times 400}{4} = 10 m/s$

$a = \frac{μ m g}{m} = μ g$

$Apply equation of motion, v^{2} = u^{2} + 2 a s$

$\Rightarrow 0^{2} = {(10)}^{2} - 2 μ g \times 20$

$\Rightarrow 40 μ g = 100$

$\Rightarrow μ = \frac{100}{2 \times 10 \times 20} = \frac{1}{4}$

Q 9 :

A particle of mass $m$ moving with velocity $v$ collides with a stationary particle of mass $2 m$ . After collision, they stick together and continue to move together with velocity ______. [2023]

$v$
$\frac{v}{2}$
$\frac{v}{3}$
$\frac{v}{4}$

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(3)

[IMAGE 46]

$Applying conservation of linear momentum$

$\Rightarrow {\vec{P}}_{i} = {\vec{P}}_{f}$

$m v + 2 m \times 0 = (3 m) v'$

$∴$ $m v = 3 m v' \Rightarrow v' = \frac{v}{3}$

Q 10 :

A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before collision is ________ ${ms}^{- 1}$ . [2023]

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(4)

[IMAGE 47]

$1 \times u_{1} = - 2 + 3 v$

$\Rightarrow u_{1} = - 2 + 3 v$ ...(i)

$1 = \frac{v + 2}{u_{1}} \Rightarrow v + 2 = u_{1}$ ...(ii)

$Solving (i) and (ii), u_{1} = 4 m/s$

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]

Q 9 :

A particle of mass $m$ moving with velocity $v$ collides with a stationary particle of mass $2 m$ . After collision, they stick together and continue to move together with velocity ______. [2023]

Q 10 :

A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before collision is ________ ${ms}^{- 1}$ . [2023]

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