question_answer

A ball is thrown vertically downwards from a height of 20m with an initial velocity\[{{V}_{{}^\circ }}\]. It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity \[{{V}_{{}^\circ }}\] is:

A) 28m/s                           

B) 10m/s

C) 14m/s                           

D) 20m/s

Correct Answer: D

Solution :

[d] When it hits the ground \[TE=\frac{1}{2}mv_{0}^{2}+mgh\] It loses 50% energy, it left with 50% energy, this left energy converted into potential energy \[\frac{50}{100}\left[ \frac{1}{2}mv_{0}^{2}+mgh \right]=mgh\] \[mv_{0}^{2}+2\,mgh=4\,mgh\,\] \[v_{0}^{2}+2\,gh\] \[v_{0}^{2}+2\times 10\times 20\] \[v_{0}^{2}=400\] \[v_{0}^{2}=20m/s\]