Question

The kinetic energy of a moving body of linear momentum p is doubled .The final momentum of the body is (by using p=mv)

Answer 1

K.E=P^2/2m
P=/~K.E 2m
K.E is doubled
P=/~2K.E 2m
P=/~2P
so the final momentum of the body increases by the factor underroot 2

Answer 2

The new momentum of the body becomes $\sqrt{2}$ times of the initial momentum.

Explanation:

The relation between the kinetic energy and the linear momentum is given by :

$E=\dfrac{p^2}{2m}$

$p=\sqrt{2mE}$

p is the momentum of the body

m is the mass of the body

If kinetic energy is doubled, E' = 2E, the final momentum of the body will be given by :

$p'=\sqrt{2mE'}$

$p'=\sqrt{2m(2E)}$

$p'=\sqrt{2} \times \sqrt{2mE}$

$p'=\sqrt{2} p$

So, the new momentum of the body becomes $\sqrt{2}$ times of the initial momentum. Hence, this is the required solution.

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