Two bodies $A$ and $B$ have 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 $1 : 3$
$\frac{m_{1}}{m_{2}} = \frac{3}{1}$ and $\frac{K E_{1}}{K E_{2}} = \frac{1}{3}$
$\frac{\frac{1}{2} m_{1} {v^{2}}_{1}}{\frac{1}{2} m_{2} {v^{2}}_{2}} = \frac{1}{3} \frac{m_{1}}{m_{2}} λ {(\frac{v_{1}}{v_{2}})}^{2} = \frac{1}{3} 3 {(\frac{v_{1}}{v_{2}})}^{2} = \frac{1}{3} \frac{v_{1}}{v_{2}} = \sqrt{\frac{1}{9}} = 1 : 3$

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