Question

If the kinetic energy of body becomes 256 times of its initial value, then new momentum will

Answer 1

relation between kinetic energy and linear momentum is given by ,
$\qquad K.E=\frac{P^2}{2m}$
where K.E is kinetic energy , m is mass of body and P is linear momentum.
if m remains constant.
then, $K.E\propto P^2$

$\frac{K.E_1}{K.E_2}=\frac{P_1^2}{P_2^2}$

A/C to question,
kinetic energy of body becomes 256 times of its initial value.
Let initial kinetic energy is K
then, final kinetic energy is 256K.
now, $\frac{1}{256}=\frac{P_1^2}{P_2^2}$

$\frac{P_1}{P_2}=\sqrt{\frac{1}{16^2}}=\frac{1}{16}$
hence, final linear momentum is 16 times of its initial value.