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 impar…

Question

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):

1. A. 21 NS (Correct answer)
2. B. 7 NS
3. C. 0
4. D. 84 NS

Correct Answer

Option A — 21 NS

Detailed Solution & Explanation

The correct answer is 21 NS.

Key Points

• Speed just before impact: $v_1=\sqrt{2gh_1}=\sqrt{2\times9.8\times40}=\sqrt{784}=28$ m s$^{-1}$ (downward).
• Speed just after impact: $v_2=\sqrt{2gh_2}=\sqrt{2\times9.8\times10}=\sqrt{196}=14$ m s$^{-1}$ (upward).
• Impulse $=\Delta p=m(v_2-v_1)=0.5\times\big(14-(-28)\big)=0.5\times42=21$ N s.