A body of mass `m_(1) = 4kg moves at `5 hat(i) ms^(-1)` and another body of mass `m_(2) = 2kg` moves at `10hat(i)ms^(-1)`. The kinetic energy of center of mass is

Options

A. `200/3J`
B. `500/3J`
C. `400/3J`
D. `800/3J`

Answer

C

Explanation

`v_(CM) = (m_(1)(dr_(1))/(dt)+m_(2)(dr_(2))/dt)/(m_(1) + m_(2)) = (4 xx 5hat(i) + 2 xx 10hat(j))/(4+2)`
`v_(CM) = (40hat(i))/6 = 20/3hat(i)`
The kinetic energy,
`K = 1/2mv^(2) = 1/2xx(4+2) xx(20 xx 20)/(3 xx 3)`
`=1/2 x 6 xx (20 xx 20)/(3 xx 3) = 400/3 J`