We have,

(K.E.)_{1}= P^{2}/2m

Where ‘P’ is momentum and ‘m’ is the mass of the object.

If the momentum is doubled then,

(K.E.)_{2} = (2P)^{2}/2m

Or, (K.E.)_{2} = 4(K.E.)_{1}

Therefore, on doubling the momentum, the K.E. of the body increases by four times its initial K.E.

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