An equilateral prism of mass m rests on a rough horizontal surface with cofficent of friction `mu`. A horizontal force F is applied on the prism as shown in the figure. If the cofficent of the friction is sufficently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is

Options

A. `(mg)/sqrt(3)`
B. `(mg)/4`
C. `(mumg)/(sqrt(3))`
D. `(mumg)/4`

Answer

A

Explanation

The tendency of rotating will be about point `C`. For the minimum force, the torque of `F` about `C` has to be equal to the torque of `mg` about `C`.

`F(a (sqrt(3))/2)=mg(a/2)impliesF=(mg)/(sqrt(3))`