Question

A spherical ball of mass m is kept at the highest point in the spacebetween two fixed, concentric spheres A and B (see figure). Thesmaller sphere A has a radius R and the space between the twospheres has a width d. The ball has a diameter very slightly lessthan d. All surfaces are frictionless. The ball given a gentle push(towards the right in the figure). The angle made by the radius vec-tor of the ball with the upward vertical isrepresented by  (shown in figure)

Answer 1

Answer:

N = mg(3cos Θ - 2)

Explanation:

Let h be the difference in height when the ball is pushed from the highest point till the other position as can be see in the figure.

H = ( R + d/2) ( 1- cos Θ)

Velocity of the ball at angle θ

V = 2gh;

Substituting the value of h;

V= 2g ( R + d/2) ( 1- cos Θ)

Let N be the normal reaction (away from the centre.....there is only one centre) at angle θ. Then

Mgcos θ – N = mv^2/( R + d/2)

Substituting the value of v^2, we get;

Mgcos θ – N = 2mg(1- cos Θ)

N = mg(3cos Θ - 2)