Question

elastic balls are placed at rest on a smooth horizontal plane which is circular at the ends with radius as shown in the figure. The masses of the balls are respectively. What is the minimum velocity which should be imparted to the first ball of mass such that ball completes the vertical circle:

117849
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A

B

C

D

Hard

Solution

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Correct option is A)

Using the expressions forΒ  velocities of the two particles in one dimensional elastic collision,

;

Velocity of the second ball ;
Let velocity of the first ball ;
For collision between the first and second ball,

;

The second ball will have a elastic collision with the third ball.
Since the ratio of consecutive masses of the balls is same, the velocity ratio of the ball will be same.

;

Continuing this for the n-th ball, we get

;

From motion of a particle in a vertical circle, the minimum velocity required for the particle to reach the highest point on the vertical circle is ;

;

;

.

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