JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Work, Power & Energy

A body is dropped on ground from a height '

h_{1}

' and after hitting the ground, it rebounds to a height '

h_{2}

'. 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

\frac{x}{4}

. The value of

x

is ____.

Answer: 375

Solution

Let

V_{1}

and

V_{2}

be the speeds just before and just after impact, with

\frac{V _{1}}{V _{2}} = 4

. The fractional loss of kinetic energy is

1 - \frac{\frac{1}{2} m V _{2}^{2}}{\frac{1}{2} m V _{1}^{2}} = 1 - (\frac{V _{2}}{V _{1}})^{2} = 1 - \frac{1}{16} = \frac{15}{16}

. As a percentage this is

\frac{15}{16} \times 100 = \frac{375}{4} %

. The value of

x

375

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Integer answer

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