A spherical ball of mass m is kept at the highest point in the space between two fixed, concentric spheres A and B (see fig.). The smaller sphere A has a radius R and 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 in the figure). The angle made by the radius vector of the ball with the upward vertical is denoted by θ . What is the total normal reaction force exerted by the spheres on the ball in terms of angle θ ?

Question

A spherical ball of mass m is kept at the highest point in the space between two fixed, concentric spheres A and B (see fig.). The smaller sphere A has a radius R and 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 in the figure). The angle made by the radius vector of the ball with the upward vertical is denoted by θ . What is the total normal reaction force exerted by the spheres on the ball in terms of angle θ ?, m g ( 3 cos θ – 2 ), m g ( 2 cos θ – 3 ), 3 m g ( 2 cos θ – 1 ), 2 m g ( 3 cos θ – 1 )

MARKS App · Accepted Answer

h = R + d 2 1 - cos θ The velocity of the ball at an angle θ is ν 2 = 2 g h = 2 R + d 2 1 - cos θ g ...... (i) Let N be the normal reaction (away from the centre) at angle θ . Then, mg cos θ - N = m ν 2 R + d 2 Substituting the value of ν 2 from equation (i), we get mg cos θ - N = 2 mg 1 - cos θ N = m g 3 cos θ - 2

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