Question

A body falls freely from a height of 100 m on to the ground and rebounds to a maximum height of 36 m after collision. The coefficient of restitution between the ground and the body is:

• A. 0.4
• B. 0.36
• C. 0.6
• D. 0.5

Hint:

The coefficient of restitution is the square root of the ratio of rebound height to drop height when a body is dropped and rebounds.

Answer 1

The Correct Option is C

The body falls from a height of 100 m and rebounds to a height of 36 m after collision. The coefficient of restitution \( e \) is given by the ratio of the square root of the rebound height to the drop height: \[ e = \sqrt{\frac{h_{\text{rebound}}}{h_{\text{drop}}}} \] Substituting the values: \[ e = \sqrt{\frac{36}{100}} = \sqrt{0.36} = 0.6 \] Thus, the coefficient of restitution between the ground and the body is \( 0.6 \).

Answer 2

Step 1: Understand coefficient of restitution.
The coefficient of restitution \( e \) is the ratio of the speed after collision to the speed before collision (along the line of impact):
\[ e = \sqrt{\frac{\text{height after rebound}}{\text{height before impact}}} \]
Step 2: Substitute the given values.
\[ e = \sqrt{\frac{36}{100}} = \sqrt{0.36} = 0.6 \]
Final Answer: \( \boxed{0.6} \)