Question

Consider the situation in which three identical spheres of clay are launched simultaneously, one along each possible path. All three spheres of clay are launched with the same initial linear speed and collide with the rod at the same time. The time of collision with the rod for each sphere is time t0. Which of the following predictions is correct about the motion of the system containing the rod and all three spheres of clay immediately after the collision?

a. The system will rotate in the clockwise direction with a constant angular speed.
b. The system will rotate in the counterclockwise direction with a constant angular speed.
c. The system will rotate in the clockwise direction with a changing angular speed.
d. The system will rotate in the counterclockwise direction with a changing angular speed.

Answer 1

a. The system will rotate in the clockwise direction with a constant angular speed.

Step-by-step explanation:

As all the clay is identical sphere and there will be hence same mass 'm' for all three clay spheres. Now their identical speed 'v' and collision time
`$'t_0'$` are also same. So all the spheres will exert same force F on the rod.

`$f=(mv)/(t_0)$`

Force exerted by the clay Z on rod is passing through pivot, so no torque will be produced.

Now clay X will collide at near distance from pivot than that of clay Y.

So clay Y will produce more torque than clay X. So clay Y will give more clockwise torque. So rod will rotate clockwise.

Now in any impact because net force and net torque are zero (because in impact torque and force occurs in equal and opposite pairs). So net angular momentum will be conserved and hence angular speed will be constant.

Therefore it is clear that option (a) is correct.