A uniform solid sphere of mass M and radius R is lying on a rough horizontal plane. A constant force F = 4 M g acts vertically downwards at point P such that the line OP makes an angle of 60 ° with th

Question

A uniform solid sphere of mass M and radius R is lying on a rough horizontal plane. A constant force F = 4 M g acts vertically downwards at point P such that the line OP makes an angle of 60 ° with the horizontal as shown in the figure. The minimum value of the coefficient of friction μ so that sphere performs pure rolling, is

TestHub · Accepted Answer

Writing torque about the bottommost point, 4 M g × R 2 = 7 5 M R 2 a R ⇒ a = 10 g 7 f = μ 5 M g = M a 5 μ g = 10 g 7 ⇒ μ = 2 7

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