A uniform rod of mass `M = 6m` and length L is at rest on a frictionless surface. Two particles of mass `2m` and `4m`, moving with velocity `(v)/(2) m//s` and `(v)/(4)m//s` respectively strikes perpendicular to the rod form the same direction at its extreme ends and sticks to the rod. Find the distance travelled by the rod in time t.

Options

A. `(vt)/(6)`
B. `(vt)/(4)`
C. `vt`
D. `6vt`

Answer

A

Explanation

COAM, `2m (v)/(2) (L)/(4) - 4m (v)/(4) (L)/(4) = I omega, omega_(cm) = 0`
COLM, `2m (v)/(2) + 4m (v)/(4) = (M + 6m) V_(cm)`

`2mv = (M + 6m) V_(cm)`
`(2mv)/((M + 6m)) = V_(cm)`
`S = (2 mv)/((M + 6m)) t rArr s = (vt)/(6)`