A ball is dropped onto a horizontal floor. It reaches a height of $144 c m$ on the first bounce and $81 c m$ on the second bounce. The coefficient of restitution is

0

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0.75

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\frac{81}{44}

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1

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Solution

The correct option is C $0.75$
Initial velocity after first bounce $= \sqrt{2 g h_{1}}$
Initial velocity after second bounce $= \sqrt{2 g h_{2}}$
now considering second collision
before after
$↓ \sqrt{2 g h_{1}}$ $\to$ $↑ \sqrt{2 g h_{2}}$

$e = \frac{\sqrt{2 g h_{2}} - 0}{0 + \sqrt{2 g h_{1}}}$

$e = \sqrt{\frac{h_{2}}{h_{1}}}$

$= \sqrt{\frac{81}{144}}$

$= \frac{9}{12} = 0.75$

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A ball is dropped onto a horizontal floor. It reaches a height of 144cm on the first bounce and 81cm on the second bounce. The coefficient of restitution is

The correct option is C 0.75Initial velocity after first bounce =√2gh1Initial velocity after second bounce =√2gh2now considering second collisionbefore after↓√2gh1 → ↑√2gh2e=√2gh2−00+√2gh1e=√h2h1=√81144=912=0.75

A ball is dropped onto a horizontal floor. It reaches a height of $144 c m$ on the first bounce and $81 c m$ on the second bounce. The coefficient of restitution is