A body is dropped on ground from a height ‘h₁’ and after hitting the ground it rebounds to a height ‘h₂’. If the ratio of velocities of the body just before and after hitting ground is 4,then percentage loss in kinetic energy of the body is x/4. The value of x is

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answer is 375.

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Detailed Solution

Loss in $KE \frac{ΔKE}{KE} = \frac{h_{1} - h_{2}}{h_{1}}$
$\begin{array}{l} \frac{ΔKE}{KE} = 1 - \frac{h_{2}}{h_{1}} \end{array}$

$\begin{array}{l} \frac{x}{4} = [1 - {(\frac{v_{2}}{v_{1}})}^{2}] \times 100, \end{array}$

$\frac{x}{4} = [1 - {(\frac{1}{4})}^{2}] \times 100$

$\begin{array}{l} \frac{x}{4} = (1 - \frac{1}{16}) \times 100, \frac{x}{4} = \frac{15}{16} \times 100 \end{array}$

$x = \frac{15}{4} \times 100, x = 375$

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