A square plate of side 'a' and mass 'm' is lying on a horizontal floor. A force `F` is applied at the top. Find the maximum force that can be applied on the square plate so that the plate does not topple about A.

Explanation

For force equilibrium
`N=mg`
`f=F`
For torque equilibrium
`tau_(0)=0=F(a)/(2)+f.(a)/(2)-N(a)/(2)`
`impliesFa=mg.(a)/(2)impliesF=(mg)/(2)`
Alternatively If a body is in complete equilibrium then net torque will be zero about all the points in the universe. So lets calculate the torque about point `A`.
`Fa=mg.(a)/(2)=-F=(mg)/(2)`