Question

two masses one n times heavier than the other have equal kinetic energy,what is the ratio of their momenta?

Answer 1

hope its correct and helpful

Answer 2

Answer:

$\dfrac{P_{1}}{P_{2}}=\dfrac{1}{\sqrt{n}}$.

Explanation:

Let the mass of the first body is $x$ Kg and the mass of the second body is $nx$ Kg.

Since, it is given that both the bodies having equal K.E.

$K.E_{1}=K.E_{2}$

Where 1 and 2 used for first and second bodies respectively.

$\dfrac{x(v^{2})_{1} }{2} =\dfrac{nx(v^{2})_{2}}{2}$

$\dfrac{v_{1}}{v_{2}}}=\sqrt{n}$

Since we know that the momenta is the multiple of mass and velocity.

So,the ratio of the momenta is

$\dfrac{P_{1}}{P_{2}}=\dfrac{1}{\sqrt{n}}$.