Question

A rectangular block has a square base measuring a x a, and its height is h. It moves on a horizontal surface in a direction perpendicular to one of the edges. The coefficient of friction is μ. It will topple if

(a) μ > h/a

(b) μ > a/h

(c) μ > 2a/h

(d) μ > a/2h

Answer 1

Correct Answer is: (b) μ > a/h

Let C be the centre of mass of the block. When the force of friction acts on the block, the normal reaction (N) of the ground shifts to the right so as to balance the torque due to F about C. The condition of toppling arises when N reaches the edge of the cube. Taking torque about C, toppling occurs when 

F x h/2 > N x a/2

or μmgh > mga or μ > a/h.