two bodies of mass 1 kg and 3 kg have equal kinetic energy. Find the ratio of velocity.

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Solution

The kinetic energies for the two bodies of different masses and different velocities will be given as,
$K E_{1} = \frac{1}{2} m_{1} {v_{1}}^{2}$ and $K E_{2} = \frac{1}{2} m_{2} {v_{2}}^{2}$
Now, as $K E_{1} = K E_{2}$ , therefore on comparing both the equations we get,
$\frac{1}{2} m_{1} {v_{1}}^{2} = \frac{1}{2} m_{2} {v_{2}}^{2} m_{1} {v_{1}}^{2} = m_{2} {v_{2}}^{2} \frac{{v_{1}}^{2}}{{v_{2}}^{2}} = \frac{m_{2}}{m_{1}} \frac{v_{1}}{v_{2}} = \sqrt{\frac{m_{2}}{m_{1}}}$
On substituting the values we get,
$\frac{v_{1}}{v_{2}} = \sqrt{\frac{3 k g}{1 k g}} \frac{v_{1}}{v_{2}} = \frac{\sqrt{3}}{1} \frac{v_{1}}{v_{2}} = 1.732$
Thus, the ratio of their velocities will be, $v$ ₁:v₂=3:1

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