Question

A uniform cube of side $l$ and mass $m$ rests on a rough horizontal table. A horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of the face at a height $3l/4$ above the base. Assuming that the cube may tip about an edge without slipping, find the angular acceleration of the cube when $F$ is equal to (a) $mg/3$, and (b) $mg$.

Answer 1

In the figure given in the attachment, the direction of forces has been shown. Normal force shift to the edge.By taking moments at P we will get;
F×3a/4=mg a/2
F= mg a/2 x 4/3a
F=2/3mg

Hence, when F=

a) mg/3 there is no angular accelaration