A heavy and a light object have the same momentum. Which one has a larger kinetic energy?

Heavier object

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Lighter object

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Both are equal

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Cannot be determined

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Solution

The correct option is C Lighter object
$light object p_{1} = m_{1} v_{1}$ and heavy object $p_{2} = m_{2} v_{2}$
But $p_{1} = p_{2}$
$(K . E)_{1} = \frac{1}{2} m_{1} v_{1}^{2}, (K . E)_{2} = \frac{1}{2} m_{1} v_{2}^{2}$
$(K . E)_{1} = \frac{1}{2 m_{1}} p_{1}^{2}$
$(K . E)_{2} = \frac{1}{2 m_{2}} p_{2}^{2}$

$\frac{(K . E)_{1}}{(K . E)_{2}} = \frac{m_{2}}{m_{1}}$

But $m_{1} < m_{2}$
Therefore, $(K . E .)_{1} > {(K . E .)}_{2}$

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A heavy and a light object have the same momentum. Which one has a larger kinetic energy?

The correct option is C Lighter objectlight object p1=m1v1and heavy object p2=m2v2But p1=p2 (K.E)1=12m1v21 ,(K.E)2=12m1v22(K.E)1=12m1p21 (K.E)2=12m2p22(K.E)1(K.E)2=m2m1But m1<m2Therefore, (K.E.)1>(K.E.)2