Question

A body is just being revolved in a vertical circle of radius R with a uniform speed. The string breaks when the body is at the highest point. The horizontal distance covered by the body after the string breaks is

• A. 2 R
• B. R
• C. R $\sqrt 2$
• D. 4R

Answer 1

Answer: (A)

2 R

Answer 2

As the body just completes the circular path, hence critical speed at the highest point. $v_H = \sqrt{ gR }$ which is totally horizontal. As the string breaks at the highest point, hence from here onward the body will follow parabolic path. Time taken by the body to reach the ground t = $\sqrt{ \frac{ 2 h }{ g } } = \sqrt{ \frac{ 2 \times 2 R }{ g }}$ Hence, horizontal distance covered by the body = $v_H \times t = \sqrt { gR } \times \sqrt{ \frac{ 4R }{ g }} = 2 R$