Two bodies of masses 3m and 9m are moving with equal kinetic energies. The ratio of linear momenta is:

Options

A. `1:3`
B. `1:sqrt(3)`
C. `3:1`
D. `sqrt(3):1`

Answer

B

Explanation

`P=mv`
`therefore (P_(1))/(P_(2))=(m_(1)v_(1))/(m_(2)v_(2))`
`K.E.=(1)/(2)m_(1)v_(1)^(2)`
`=(1)/(2)m_(2)v_(2)^(2)`= Constant
`therefore (v_(1)^(2))/(v_(2)^(2))=(m_(2))/(m_(1))=(9m)/(3m)=(3)/(1)`
`(v_(1))/(v_(2))=(sqrt(3))/(1)`
`(P_(1))/(P_(2))=(m_(1)v_(1))/(m_(2)v_(2))=(3m)/(9m)xx(sqrt(3))/(1)`
`=(3sqrt(3))/(9xx1)=(sqrt(3))/(3)`
`=(sqrt(3))/(sqrt(3)xxsqrt(3))=(1)/(sqrt(3))`
`therefore P_(1):P_(2)=1:sqrt(3)`