question_answer

A ball is falling freely from a height. When, it reaches 10 m height from the ground its velocity is \[{{v}_{0}}\]. It collides with the ground and loses 50% of its energy and rises back to height of 10 m. Then, the velocity\[{{v}_{0}}\]is

A)  7 m/s                   

B)  10 m/s

C)  14 m/s                

D)  16 m/s

Correct Answer: C

Solution :

                At height 10 m, the kinetic energy is equal to potential energy, then \[\frac{1}{2}mv_{0}^{2}=mgh\] \[\frac{1}{2}v_{0}^{2}=9.8\times 10\]     \[v_{0}^{2}=2\times 9.8\times 10\]     \[{{v}_{0}}=\sqrt{196}\]     \[{{v}_{0}}=14\,m\text{/}s\]