Physics Q10 – NEET-UG 2025

Home Physics Laws of MotionQuestion #220

A ball of mass

0.5 kg

is dropped from a height of

40 m

. The ball hits the ground and rises to a height of

10 m

. The impulse imparted to the ball during its collision with the ground is (Take

g = 9.8 {m/s}^{2}

)

Clue 1 of 3: Impulse-Momentum Theorem

Impulse is defined as the change in momentum of an object.

🧠 Full Solution Path

● Video Walkthrough

Step 1: Calculate velocities before and after collision✦ Active

First, calculate the velocity of the ball just before it hits the ground ( $v_{1}$ ) using the initial height $h_{1} = 40 m$ . Since it's dropped, the initial velocity is $0$ . Using the kinematic equation $v^{2} = u^{2} + 2 g h$ , we get $v_{1} = \sqrt{2 g h_{1}}$ .

v_{1} = \sqrt{2 \times 9.8 {m/s}^{2} \times 40 m} = \sqrt{784} m/s = 28 m/s (downwards)

Next, calculate the velocity of the ball just after it rebounds from the ground ( $v_{2}$ ) using the rebound height $h_{2} = 10 m$ . At the peak of its rebound, its final velocity is $0$ . Using $v^{2} = u^{2} + 2 g h$ , we get $v_{2} = \sqrt{2 g h_{2}}$ .

v_{2} = \sqrt{2 \times 9.8 {m/s}^{2} \times 10 m} = \sqrt{196} m/s = 14 m/s (upwards)

💡 Teacher's Secret Hint

Ensure you use the correct height for each velocity calculation. $g$ is positive when calculating speed due to fall or speed needed to reach a height.

Step 2: Calculate the change in momentum (Impulse)○ Expand

Impulse ( $J$ ) is the change in momentum, $J = Δ p = m (v_{f} - v_{i})$ . It's crucial to consider the direction of velocities. Let's take the upward direction as positive and the downward direction as negative.

Initial velocity (before collision) $v_{i} = - 28 m/s$ (downwards).

Final velocity (after collision) $v_{f} = + 14 m/s$ (upwards).

J = m (v_{f} - v_{i}) = 0.5 kg \times (14 m/s - (- 28 m/s))

J = 0.5 kg \times (14 + 28) m/s = 0.5 kg \times 42 m/s

J = 21 NS

💡 Teacher's Secret Hint

The most common mistake is forgetting the vector nature of velocity and momentum. Always assign a consistent sign convention for directions.

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Physics Question 10 – NEET-UG 2025

Clue 1 of 3: Impulse-Momentum Theorem

🧠 Full Solution Path