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A solid sphere of mass 0.50 kg is kept o...

A solid sphere of mass 0.50 kg is kept on a horizontal surface. The coefficient of static friction between the surfaces in contact is 2/7. What maximum force can be applied at the highest point in the horizontal direction so that the sphere does not slip on the surface?

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The correct Answer is:
C
If we take moment about the center than
`FxxR=Ialpha+fxxR`
`rarr F=2/5mRalpha+mumg`…….1
`Again F=ma_c-m mg`…….. 2
`-[because a_c=ralpha]`
`rarr a=((F+mumg))/m`
Putting the value of `a_c` in equation 1 we get
`=(2/5)(F+mug)/m+mu mg`
`rarr F=2/5F+2/5+2/5xx2/7xx0.5xx10+2.7xx0.5xx10`
`rarr (3F)/5=4/7+10/7=2`
`rarr F=((5x2))/3=10/3=3.3N`
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