Two bodies $A$ and $B$ and their masses in the ratio $3 : 1$ and kinetic energy in the ratio $1 : 3$ , then ratio of their velocities is

1 : 1

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1 : 3

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3 : 1

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1 : \sqrt{3}

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Solution

The correct option is B $1 : 3$
$m_{1} = 3 m_{2}$
$\frac{1}{2} m_{1} v_{1}^{2} = \frac{1}{3} (\frac{1}{2} m_{2} v_{2}^{2}) . . (1)$
By using equation (1),
$3 m_{2} v_{1}^{2} = \frac{1}{3} m_{2} v_{2}^{2}$
$\frac{v_{1}}{v_{2}} = 1 : 3$

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