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A sphercial ball of mass m is kept at th...

A sphercial ball of mass m is kept at the highest point in the space between two fixed, concentric spheres A and B (figure). The small sphere A has a radius R, and the space between the two spheres has a width d. The ball has a diameter very slightly less than d. All surfaces are frictionless. The ball is given a gentle push (towards the right figure). The angle made by the radius vector of the ball with the upward vertical is denoted by `theta` (shown in figure).

a. Express the total normal reaction force exerted by the sphere on the ball as a function of angle `theta`.
b. Let `N_A` and `N_B` denote the magnitudes of the normal reaction forces on the ball exerted by spheres A and B, respectively. Sketch the variations of `N_A` and `N_B` as functions of `cos theta` in the range `0lethetalepi` by drawing two separate graphs in your answer book, taking `cos theta` on the horizontal axes.

A

`mg(3 cos theta-2)`

B

`mg (2 cos theta-3)`

C

`3mg (2 cos theta-1)`

D

`2mg (3 cos theta-1)`

Text Solution

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The correct Answer is:
A
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