Work Energy and Power - Result Question 25
28. A rubber ball is dropped from a height of $5 m$ on a plane, where the acceleration due to gravity is not shown. On bouncing it rises to $1.8 m$. The ball loses its velocity on bouncing by a factor of
[1998]
(a) $\frac{16}{25}$
(b) $\frac{2}{5}$
(c) $\frac{3}{5}$
(d) $\frac{9}{25}$
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Answer:
Correct Answer: 28. (b)
Solution:
- (b) According to principle of conservation of energy,
Loss in potential energy $=$ Gain in kinetic energy
$\Rightarrow m g h=\frac{1}{2} m v^{2} \Rightarrow v=\sqrt{2 g h}$
If $h_1$ and $h_2$ are initial and final heights, then $v_1=\sqrt{2 g h_1}$ and $v_2=\sqrt{2 g h_2}$ Loss in velocity,
$\Delta v=v_1-v_2=\sqrt{2 g h_1}-\sqrt{2 g h_2}$
$\therefore$ Fractional loss in velocity,
$=\frac{\Delta v}{v_1}=\frac{\sqrt{2 g h_1}-\sqrt{2 g h_2}}{\sqrt{2 g h_1}}=1-\sqrt{\frac{h_2}{h_1}}$
$=1-\sqrt{\frac{1.8}{5}}=1-\sqrt{0.36}=1-0.6=0.4=\frac{2}{5}$
