A solid sphere of mass 5kg and radius 1m is kept on a rough surface. A force F=30N is acting at the top most point. Friction required for pure rolling is
A
70/9N
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B
90/7N
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C
90/5N
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D
50/9N
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Solution
The correct option is B90/7N Let us suppose force of friction required is f and will act in forward direction as sphere has tendency to slip back when F=30N is applied. On taking instantaneous axis of rotation about bottom most point.
On applying ∑T=Iα 30×2=(25×5×12+5×12)α[T=Fr⊥=Iα,I=Io+md2] ⇒α=607rad/s ... (1) We know, for pure rolling, a=αR ⇒a=607m/s... (2) [from (1) and R=1m] On applying ∑F=ma along horizontal, ⇒30+f=5×607 [from (2)] ⇒f=907N