A horizontal force `F` is applied at the centre of solid sphere placed over a plank. The minimum coefficient of friction between plank and sphere required for pure rolling is `mu_(1)` when plank is kept at rest ad `mu_(2)` when plank can move, then `mu_(2)ltmu_(1)`
Reason: Work done by frictional force on the sphere in both cases is zero.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

C. If assertion is true, but the reaction is false.
D. If assertion is false but the reason is true.

Explanation

In first case
`a=Ralpha`
`therefore(F-mu_(1)mg)/(m)=R((mu_(1)mR)/(2//5mR^(2)))`
`=(5)/(2)mu_(1)g` or `mu_(1)=(2)/(7)(F)/(mg)`
In second case, ,brgt `a-Ralpha=a_("plank")`
`therefore((F-mu_(2)mg)/(m))-R((mu_(2)mg)/(2//5mR^(2)))=(mu_(2)mg)/(M)`
`therefore(F)/(m)=mu_(2)g+(5)/(2)mu_(2)g+(m)/(M)mu_(2)g`
`thereforemu_(2)=(F)/((7//2+(m)/(M))mg)`
Net work done by friction in pure rolling is zero.