How does K.E. of an object change if its momentum is doubled?

# How does K.E. of an object change if its momentum is doubled?

We have,

(K.E.)

_{1}= P^{2}/2m

Where â€˜Pâ€™ is momentum and â€˜mâ€™ 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.