Two particle of masses `m_1 and m_2` have equal kinetic energies . The ratio of their momenta is

Options

A. `m_1 : m_2`
B. `m_2 : m_1`
C. `sqrtm_1 : sqrtm_2`
D. `m_1^2:m_2^2`

Answer

C

Explanation

The kinetic energy K and momentum p of a particle are related by the relation
`K=p^2/(2m)` where m is the mass of the particle
So `K_1=P_1^2/(2m_1) and K_2=(P_2^2)/(2m_2)`
But as per question `K_1 = K_2`
`:.P_1^2/(2m_1)=(P_2^2)/(2m_2)" or "P_1^2/P_2^2=m_1/m_2 " or "P_1/P_2=sqrt((m_1)/m_2)`