Question

Two bodies A and B having mass ratio 1 : 4 have same kinetic energy. Which will have higher momentum?

Answer 1

A has large momentum using formula of kinetic energy

Answer 2

Given that,

Ratio of masses of two bodies A and B is 1:4.

To find,

Which will have higher momentum?

Solution,

The relation between kinetic energy and the momentum of an object is given by :

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

p is momentum

m is mass

Both bodies have same kinetic energy

$\dfrac{p_A}{p_B}=\sqrt{\dfrac{2m_A}{2m_A}} \\\\\dfrac{p_A}{p_B}=\sqrt{\dfrac{m_A}{m_B}} \\\\\dfrac{p_A}{p_B}=\sqrt{\dfrac{1}{4}} \\\\\dfrac{p_A}{p_B}=\dfrac{1}{2}$

So, the ratio of momentum of the bodies is 1:2. It shows that momentum of body B is more than that of B.

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