A sphere can roll on a surface inclined at an angle provided that the friction coefficient is greater than 2 7 . Assume the friction coefficient is given by 1 7 g . If a sphere is released from rest on this inclined surface,

Step-by-step solution

When the sphere is released on the inclined plane, the component of gravity along the incline is mg , which tends to slide the sphere downwards. Since the coefficient of friction is non-zero (given as = 1 7 g or assuming a typo for 1 7 ), a frictional force will act on the sphere at the point of contact in the upward direction along the incline. This frictional force provides a torque about the centre of mass of the sphere ( = f R ), which produces an angular acceleration. Thus, the sphere will rotate about its cen