A solid sphere of mass `m` is lying at rest on a rough horizontal surface. The coefficient of friction between the ground and sphere is `mu`. The maximum value of `F`, so that the sphere will not slip, is equal to

Options

A. `7/5 mu mg`
B. `4/7 mu mg`
C. `5/7 mu mg`
D. `7/2 mu mg`

Answer

D

Explanation

For `F_(max)`, spheres is just about to slip `rArr` Friction acting `=mu_(S)N`
`F-mu_(S) (mg) = ma_(cm) (a_(cm) = R alpha)`
`mu_(2)mg xx R = (2/5 mR^(2)) xx alpha`, `mu_(S) mg = 2/5 ma_(cm) rArr F("max") = 7/2 mu_(S) mg`