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Question

A horizontal force F acts on a sphere of mass M at its centre. Coefficient of friction between the ground and sphere is μ. Let the maximum force F for which there is no slipping be n2μMg. Find n.
  1. 7
  2. 6
  3. 3
  4. 5


Solution

The correct option is A 7
For linear motion, Ff=Ma.......(1)
and for rotational motion τ=Iα, for pure rolling a=Rα
fr=Iα
fr=25MR2×aR
f=25Ma
Ma=52f......(2)
Putting equation (2) in equation (1)
f=27F
For no slipping, fμMg
2F7μMg
F72μMg
Thus, n=7.

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