How will the momentum of a body change if its K.E. is doubled ?

Explanation

We know that, `K = (p^2)/(2m) " " ....(i)`
Let `K_1` = New kinetic energy of the body.
`p_1` = New momentum of body.
Using (i), we get `K_1 = (p_1^2)/(2m)`, but `p_1 = 2p`.
Putting the value of `P_1` in equation (ii), we get, that is `K_1 = ((2p)^2)/(2m) implies K_1 = (4p^2)/(2m) = 4K`
Hence K.E. becomes four times, if momentum is doubled.