A cubical block of side rests on a rough horizontal surface with coefficient of friction . A horizontal force 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 min

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 [2000]

Smart Achievers · Accepted Answer

(3)

Here, due to applied force normal reaction shifts to one corner. At this situation, the cubical block starts toppling about point O. About point O torque

$F \times L = m g \times \frac{L}{2} \Rightarrow F = \frac{m g}{2}$

Hence minimum force required to topple the block,

$F = \frac{m g}{2}$

Solution

1 infinitesimal

2 $\frac{m g}{4}$

3 $\frac{m g}{2}$

4 $m g (1 - μ)$

Want Us to Email you About Special Offers & Updates?

Solution

1 infinitesimal

2 mg4

3 mg2

4 mg(1-μ)

Ans. (3) Here, due to applied force normal reaction shifts to one corner. At this situation, the cubical block starts toppling about point O. About point O torque F×L=mg×L2 ⇒ F=mg2 Hence minimum force required to topple the block, F=mg2

Want Us to Email you About Special Offers & Updates?

2 $\frac{m g}{4}$

3 $\frac{m g}{2}$

4 $m g (1 - μ)$