On a smooth horizontal tanle, a sphere is pressed by blocks `A` and `B` by forces `F_(1)` and `F_(2)` respectively `(F_(1)gtF_(2))` exactely normal to the tangent at the point of contact of blocks and sphere. A force `F` is applied on the sphere diameter `OP`, which is line of action of forces `F_(1)` and `F_(2)`. the sphere moves out of blocks `A` and `B`. find minimum value of `F`. the coefficient of friction is `mu` at all contancts.

Options

A. `(mu)/2(7F_(1)-3F_(2))`
B. `(mu)/2(5F_(1)-3F_(2))`
C. `mu(3F_(1)-F_(2))`
D. `(mu)/2(3F_(1)-F_(2))`

Answer

A

Explanation

`N_(1)=F_(1)` and `f_(i)=muN_(1)=muF_(1)`
`f_(2)=muF_(2), F-f_(1)-f_(2)=mato(1)`
`alpha=((f_(1)-f_(2))R)/I=(5(f_(1)-f_(2))R)/(2mR^(2))=(5(f_(1)-f_(2))/(2mR)`
`a =alphaR=5(f_91)-f_(2))//2m`
From eq. (1)
`F-f_(1)-f_(2)=(5(f_(1)-f_(2)))/2`
`F=5/2f_(1)-5/2f_(2)+f_(1)+f_(2)=(mu)/2(7F_(1)-3F_(2))`