Question

A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force F is applied normal to one of the faces at a point directly above the centre of the face, at a height 3a/4 above the base. The minimum value of F for which the cube begins to topple on an edge is (assume the cube does not slide): \includegraphics[width=0.5\linewidth]8.png

• A. (mg)/(3)
• B. (mg)/(2)
• C. (2mg)/(3)
• D. (3mg)/(4)

Hint:

For toppling problems, always take moments about the edge of rotation.

Answer 1

The Correct Option is B

Step 1: At the point of toppling, torque about the edge is balanced.
Step 2: Torque due to applied force, F × (3a)/(4)
Step 3: Torque due to weight, mg × (a)/(2)
Step 4: Equating torques, F · (3a)/(4) = mg · (a)/(2)
Step 5: Solving, F = (mg)/(2)