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 the point directly below the centre of the face, at a height $a/4$ above the base. Then,

• A. minimum value of $F$ for which the cube begins to tip about the edge is $2mg$
• B. minimum value of ${\mu }_s$ so that toppling occurs is 0
• C. minimum ${\mu }_s$ so that $F_{min}$ can cause toppling is 2
• D. minimum ${\mu }_s$ so that $F_{min}$ can cause toppling is 4

Answer 1

Answer: (A), (C)

The correct options are
A minimum value of $F$ for which the cube begins to tip about the edge is $2mg$
C minimum ${\mu }_s$ so that $F_{min}$ can cause toppling is 2

First assume, the friction is sufficient to bear the force applied.

Now applying Torque equation about toppling point of body contact,

$F_{min}\frac{a}{4}=Mg\frac{a}{2}$

$\Rightarrow F_{min}=2Mg$

For the $F_{min}$ ,${\mu }_s=\frac{F_{min}}{Mg}=2$

so ,option 1,3 is right.

And the minimum value of coeffiecient of friction is zero to topple.