A small ball of mass m and radius r = R 10 rolls without slipping along the track shown in the figure. The radius of circular part of the track is R . If the ball starts from rest at a height of 8 R above the bottom, the normal force on the ball at the point P is

Step-by-step solution

Using Work-Energy Theorem 7 mgR = 1 2 mv 2 + 1 2 2 5 mr 2 × ω 2 since the sphere is rolling without slipping v = rω ∴ 7 mgR = 1 2 ×   7 5 mr 2 ×   v 2 r 2 ⇒ v 2 = 10 gR at point P , we can consider sphere as a point object doing circular motion in a circle of the radius ( R - r ) with velocity v , Hence at point P N = mv 2 R - r = 10 mgR R - R 10 = 10 mgR 9 R 10 ( given r = R 10 ) or N = 100 9 mg