A solid sphere of mass `3 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? (in `N`)

Answer

20

Explanation

`F+f=ma` ………..i
Torque equation about point of contact
`F2R=I_(P) alpha`
`F2R=(2/5mR^(2)+mR^(2))alpha`
`F=7/10mRalpha`………….ii

From no sliding case `a =Ralpha`………….iii
From ii and iii `a=(10F)/(7m)`.........iv
From i and iv `F+f=m.(10)/(7) F/mimplies f=3/7F`
i.e friction will act in backwad direction. For no sliding
`flemuN`
`3/7Flemumgimplies fle7/3mmg`
`fle7/3xx2/7xx3xx10impliesFle20N`