Question

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

Answer 1

Correct Answer - A
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)`