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A solid sphere of mass m is lying at res...

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

A

`7/5mumg`

B

`4/7mumg`

C

`5/7mumg`

D

`7/2mumg`

Text Solution

Verified by Experts

The correct Answer is:
D
As sphere is rolling we can apply torque equation about point oif contact (about `P`).

`FR=I_Palpha`
`implies FR=(7/5MR^(2))alpha`
`impliesRalpha=(5F)/(7M)=a` (acceleration of cm)
Equation of translatory motion
`F-f=Maimplies f=2/7F`.........i
For no sliding `flemumgimpliesF=7/2mumg`
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