Two bodies of mass 1 g and 4 g moving with equal kinetic energy then the ratio of its linear momentum will be `……….`

Options

A. `4:1`
B. `sqrt(2):1`
C. `1:2`
D. `1:16`

Answer

C

Explanation

Kinetic energy `K =1/2 mv^(2)=(m^(2)v^(2))/(2m)=(p^(2))/(2m)`
Now `K_(1)=K_(2)`
`(p_(1)^(2))/(2m_(1))=(p_(2)^(2))/(2m_(2))`
` :. (p_(1))/(p_(2)) =sqrt((m_(1))/(m_(2)))=sqrt(1/4)=1/2 `
` :. (p_(1))/(p_(2)) = 1:2 `