A force `F` is applied on the top of a cube as shown in the figure. The coefficient of friction between the cube and the ground is `mu`. If `F` is gradually increased, find the value of `mu` for which the cube will topple before sliding.

Explanation

Let `m` be the mass of the cube and 'a' be the side of the side. The cube will slide if `Fgtmu mg......(1)` and it will topple if torque of `F` about `P` is gtreater than torque of `mg` about `P` i.e., `Fagt(a/2)` mg or `Fgt1/2 mg......(2)`
From equations `(1)` and `(2)` we see that cube will topple before sliding if `mu gt1/2`.