Question

A cubical block of side l rests on a rough horizontal surface with coefficient of friction μ. a horizontal force f is applied on the block as shown. if the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is

Answer 1

Final Answer : $\frac{mg}{2}$

Steps :
1) For the minimum force to topple, Normal should pass through corner vertex as in figure.
Then,

To topple, Net torque through point O must be greater than equal to 0 .
$\tau_O \geqslant 0 \\ \\ => FL - \frac{mgL}{2} + N * 0 \geqslant 0 \\ \\ => F \geqslant \frac{mg}{2}$

Hence, Minimum force required to topple the block is $\frac{mg}{2}$ .

Answer 2

Answer: Actually the answer is 2mg/3

Explanation: