A light and heavy body have equal momentum- Which one has greater kinetic energy-Light body-Heavy body-Both body have same kinetic energy-None of the above-

The correct option is A Light body Assume the weight of light body is m1 and the weight of heavy body is m2 and momentum is p1 and p2 respectively. Since momen ...

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Byju's Answer

Standard IX

Physics

Kinetic Energy

A light and h...

Question

A light and heavy body have equal momentum. Which one has greater kinetic energy?

Light body

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Heavy body

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Both body have same kinetic energy

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None of the above

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Solution

The correct option is
A

Light body

Assume the weight of light body is m₁ and the weight of heavy body is m₂ and momentum is p₁ and p₂ respectively. Since momentum is equal then p₁ = p₂

We know, Kinetic energy = $\frac{P^{2}}{2 m}$

Kinetic energy of light body = $\frac{{P_{1}}^{2}}{{2 m}_{1}}$

Kinetic energy of heavy body = $\frac{{P_{2}}^{2}}{{2 m}_{2}}$

Given p₁ = p₂

Ratio of kinetic energy of light and heavy body = $\frac{\frac{{P_{1}}^{2}}{{2 m}_{1}}}{\frac{{P_{1}}^{2}}{{2 m}_{1}}}$ = $\frac{m_{2}}{m_{1}}$

Given ( m2 > m1 )
$\frac{K E_{1}}{K E_{2}} = \frac{m_{2}}{m_{1}}$
$K E_{2} < K E_{1}$

So, the kinetic energy of lighter body is higher than the kinetic energy of heavier body.

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