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  4. A ball of mass 0.2 Kg falls under gravity from a height of 10 m with an initial velocity. It collides with the floor and looses 50 % of its energy and then rises back to the same height. The value of its initial velocity is

Q. A ball of mass $0.2 \,Kg$ falls under gravity from a height of $10 \,m$ with an initial velocity. It collides with the floor and looses $50 \%$ of its energy and then rises back to the same height. The value of its initial velocity is

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Solution:

Total energy before collision = kinetic energy $+$ potential energy
$=1 / 2\, mv ^{2}+ mgh$
After collision $=1 / 2\left(1 / 2\, m v^{2}+m g h\right)$
Since the ball rebounds to a height $10\, m $
$m g(10)=1 / 2\left(1 / 2 m v^{2}+m g(10)\right)$
$20\, g-10\, g=1 / 2 v^{2} $
$V^{2}=20\, g=20 \times 9.8=196$
$V=\sqrt{196}=14$

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