Work Energy And Power Ques 47
A ball is thrown vertically downwards from a height of $20 $ $m$ with an initial velocity $v_0$. It collides with the ground, loses $50$ percent of its energy in collision and rebounds to the same height. The initial velocity $v_0$ is : (Take $g=10$ $ ms^{-2}$ )
[2015 RS]
(a) $20 $ $ms^{-1}$
(b) $28 $ $ms^{-1}$
(c) $10\ \text{ms}^{-1}$
(d) $14 $ $ms^{-1}$
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Answer:
Correct Answer: 47.(a)
Solution:
When ball collides with the ground it loses $50 \%$ of its energy
$ \therefore \frac{KE_f}{KE_i}=\frac{1}{2} \Rightarrow \frac{\frac{1}{2} mV_f^{2}}{\frac{1}{2} mV_i^{2}}=\frac{1}{2} $
or $\frac{V_f}{V_i}=\frac{1}{\sqrt{2}}$
or, $\frac{\sqrt{2 gh}}{\sqrt{V_0^{2}+2 gh}}=\frac{1}{\sqrt{2}}$
or, $4 gh=V_0^{2}+2 gh$
$\therefore V_0=20 ms^{-1}$
BETA
