Two bodies A and B having masses in the ratio of 3 : 1 possess the same kinetic energy. The ratio of their linear momenta is then

Options

A. `1:3`
B. `3:1`
C. `sqrt3:1`
D. `1:sqrt3`

Answer

C

Explanation

According to the question, `(1)/(2) m_(1)v_(1)^(2)= (1)/(2) m_(2) v_(2)^(2)`
`rArr (m_(1))/(m_(2))= (v_(2)^(2))/(v_(1)^(2))`
Also, `(m_(1))/(m_(2))= (3)/(1)`
`therefore (m_(1)v_(1))/(m_(2)v_(2))= (m_(1))/(m_(2)) xx sqrt((m_(2))/(m_(1))) = (3)/(1) xx sqrt((1)/(3)) = sqrt3:1`