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# A solid sphere of mass m and radius R released from the top of an inclined plane such that it rolls down without slipping. If the coefficient of friction is µ and angle of inclination is ø with horizontal, then force of friction acting on the body is1)                                                                  2)               3)                                                               4)

Asked by reachrahul123 14th October 2018, 9:48 PM
Figure shows the different forces acting on the sphere that is rolling on the inclined plane.
weight mg is resolved into two components, one is perpendicular to inclined plane and
other component  is parallel to inclined plane.
Hence the normal reaction force N = mg cosΦ and the friction force is μN = μ×mg×cosΦ

All the expression given in the list of options of answer is proportional to .
if we check the units of this expression we are getting
I hope g is typed as G, m is typed as M. Similarly there is a mismatch of r and R.
I assume these typing error and considered the correct symbol.
But as explained above there is no matching of units. But I derived the correct expression for frictional force
Answered by Expert 15th October 2018, 4:56 AM
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