Question

A uniform rod of length `l` and mass `2m` rests on a smooth horizontal table. A point mass `m` moving horizontally at right angles to the rod with initial velocity `v` collides with one end of the rod and sticks to it.
Determine the position of the point on the rod which remains stationary immediately after collision.
A. The point is a distance `(1//3) l` from the end where the mass strikes.
B. The point is a distance `(2//3) l` from the end where the mass strikes.
C. The point is a distance `(2//5) l` from the end where the mass strikes
D. The point is a distance` (1//5) l` from the end where the mass strikes

Answer 1

Correct Answer - B
Form the conservation of the linear momentum.
`mv=(m+2m)v_(CM)`
`implies v+(CM)=v/3`

Let the point whose insantaneous velocity just after collisiion is zero be at a distance `I_(0)` from the centre of mass of the composite system.
`v_(CM)-l_(0)omega=0`
`implies v/3-l_(0)(v/l)=0impliesl_(0)=l/3`
The point is a distance `(2/3)l` from the end where the mass strikes.