A thin ring of mass 2kg and radius 0.5m is rolling without slipping on a horizontal plane with velocity 1m/s. A small ball of mass 0.1kg,moving with velocity 20m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision
a) |
The ring has pure rotation about its stationary |
b) |
The ring comes to a complete stop |
c) |
Friction between the ring the ground is to the left |
d) |
There is no friction between the ring and the ground |
A thin ring of mass 2kg and radius 0.5m is rolling without slipping on a horizontal plane with velocity 1m/s. A small ball of mass 0.1kg,moving with velocity 20m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision
a) |
The ring has pure rotation about its stationary |
b) |
The ring comes to a complete stop |
c) |
Friction between the ring the ground is to the left |
d) |
There is no friction between the ring and the ground |
(a,c)
The data is incomplete. Let us assume that friction from ground on ring is not impulsive during impact.
From linear momentum conservation in horizontal direction,
we have
Here, is the velocity of CM of ring after impact.
Solving the above equation, we have
Thus CM becomes stationary.
Correct answer is (a).
Linear impulse during impact
(i)In horizontal direction
(ii)In vertical direction
Writing the equation (about CM)
Angular impulse = Change in angular momentum
We have
Solving this equation becomes out ot be positive or
anti-clockwise. So just after collision rightwards slipping is taking place. Hence, friction is leftwards. Therefore, option (c) is also correct.
Correct options are (a) and (c).