Question

how will momentum of body change if its kinetic energy is dobuled

Answer 1

If momentum of a body is doubled but its mass does not increase so its velocity is doubled. If it velocity is doubled then kinetic energy increase in square2. So when momentum of a body change then kinetic energy is doubled. I think it will help you.

Answer 2

Let the mass of the body be M and the initial velocity be u.
Therefore, initial kinetic energy
$k = \frac{1}{2} m {u}^{2}$
Now the kinetic energy is doubled so let the new velocity be v.
Thus new kinetic energy
$k = \frac{1}{2} m {v}^{2}$

Now according to question
$\frac{1}{2} m {v}^{2} = 2 \times \frac{1}{2} m {u}^{2} \\ v = \sqrt{2} u$
Therefore the change in linear momentum is
$dp = m(v - u) = m( \sqrt{2}u - u) = mu( \sqrt{2} - 1)$