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(A) The relationship between kinetic energy $K$ and momentum $p$ is given by $K = \frac{p^2}{2m}$,which implies $p = \sqrt{2mK}$.Let the initial kinet

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increase twice

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(A) The relationship between kinetic energy $K$ and momentum $p$ is given by $K = \frac{p^2}{2m}$,which implies $p = \sqrt{2mK}$.Let the initial kinetic energy be $K_1 = K$ and the final kinetic energy be $K_2 = 4K$.The initial momentum is $p_1 = \sqrt{2mK_1} = \sqrt{2mK}$.The final momentum is $p_2 = \sqrt{2mK_2} = \sqrt{2m(4K)} = 2\sqrt{2mK}$.Comparing the two,we get $p_2 = 2p_1$.Therefore,the momentum increases by $2$ times.

The kinetic energy of a body is increased by $4$ times. Its momentum will

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