Work Energy And Power Question 284
Question: A rubber ball is dropped from a height of 5m on a plane, where the acceleration due to gravity is not shown. On bouncing it rises 1.Sm. The ball loses its velocity on bouncing by a factor of
Options:
A) $ \frac{16}{25} $
B) $ \frac{2}{5} $
C) $ \frac{3}{5} $
D) $ \frac{9}{25} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] According to principle of conservation of energy Potential energy = kinetic energy
$ \Rightarrow mgh =\frac{1}{2}mv^{2}\Rightarrow v =\sqrt{2gh} $ If $ {h_1}
and h_2 $ are initial and final heights, then
$ \Rightarrow v_1=\sqrt{2gh_1},v_2=\sqrt{2gh_2} $
Loss in velocity, $ \Delta v=v_1-v_2=\sqrt{2gh_1}-\sqrt{2gh_2} $
$ \therefore $ fractional loss in velocity $ =\frac{\Delta v}{v_1}=\frac{\sqrt{2gh_1}-\sqrt{2gh_2}}{\sqrt{2gh_1}}=1-\frac{h_2}{h_1} $
$ =1-\sqrt{\frac{1.8}{5}}=1-\sqrt{0.36}=1-0.6=0.4=\frac{2}{5} $
