Work Energy And Power Question 95
Question: A rubber ball is dropped from a height of 5 m on a planet where the acceleration due to gravity is not known. On bouncing, it rises to 1.8 m. The ball loses its velocity on bouncing by a factor of [CBSE PMT 1998]
Options:
A) 16/25
B) 2/5
C) 3/5
D) 9/25
Show Answer
Answer:
Correct Answer: B
Solution:
If ball falls from height $ h_1 $ and bounces back up to height $ h_2 $
then $ e=\sqrt{\frac{h_2}{h_1}} $
Similarly if the velocity of ball before and after collision are $ v_1 $ and $ v_2 $ respectively then $ e=\frac{v_2}{v_1} $
So $ \frac{v_2}{v_1}=\sqrt{\frac{h_2}{h_1}}=\sqrt{\frac{1.8}{5}}=\sqrt{\frac{9}{25}}=\frac{3}{5} $
i.e. fractional loss in velocity $ =1-\frac{v_2}{v_1}=1-\frac{3}{5}=\frac{2}{5} $
