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Question

A ball is thrown vertically downwards from a height of 20 m with an initial velocity $$\upsilon _0$$. It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity $$\upsilon _0$$ is (Take $$g=10 \,ms^{-2}$$)


A
10ms1
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B
14ms1
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C
20ms1
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D
28ms1
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Solution

The correct option is B $$20 ms^{-1}$$
Initial  energy $$E_i = PE + KE = mgh + \dfrac{1}{2}mv^2$$
Energy when it reaches the ground: $$E = \dfrac{1}{2}mv'^2$$ since PE is zero.
Given, $$E = \dfrac{1}{2}E_i$$
Since it rises to the  same height $$E_f =mgh +0$$ is the final energy
$$ \Rightarrow \dfrac{1}{2}(mgh + \dfrac{1}{2}mv^2) = E_f = mgh +0$$
$$ v^2 = 2gh = 2 \times 10 \times 20 = 20^2$$
$$ \Rightarrow v =20\:m/s$$

Physics

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