Two blocks A and B of mass $m_{A}$ and $m_{B}$ are connected together by means of a spring and are resting on a horizontal frictionless table. The blocks are then pulled apart so as to stretch the spring and then released. Show that the ratio of their kinetic energies at any instatnt is in the inverse ratio of the masses

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Solution

Since the system of two masses and the spring is not acted upon by any external force, hence the momentum should be conserved.

Initially the momentum is 0 and hence for all time the total momentum of the system should be 0.

That is $p_{A} = p_{B}$ in magnitude but opposite in direction.

Now, $K = \frac{p^{2}}{2 m}$

Since, $p =$ same.

Hence, $\frac{K_{A}}{K_{B}} = \frac{m_{B}}{m_{A}}$

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