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

Explanation

We know that, `K = (p^2)/(2m) implies p = sqrt(2mK)`
Let `p_1` be the new momentum, so `p_1 = sqrt(2mK_2) " "....(i)`
Putting `K_1 = 2K`, we get `p_1 = sqrt(2m xx 2K) =sqrt(2 xx 2mK) = sqrt(2) p`
`implies p_1 = sqrt(2) p`, hence momentum of the body becomes 2 times the initial value.
Therefore, change in momentum of body = `sqrt(2)p - p =(sqrt(2) - 1)`