Question

A block with a square base measuring $a$ and height $h$, is placed on an inclined plane. The coefficient of friction is $\mu$. The angle of inclination ($\theta$) of the plane is gradually increased. The block will

• A. topple before sliding if $\mu >\frac{a}{h}$
• B. topple before sliding if $\mu <\frac{a}{h}$
• C. slide before topping if $\mu >\frac{a}{h}$
• D. slide before topping if $\mu <\frac{a}{h}$

Answer 1

Answer: (A), (D)

slide before topping if $\mu <\frac{a}{h}$


For no slipping: $\mu N=\mu mg\cos \theta \le mg\sin \theta$
$\Rightarrow \mu \le \tan \theta$

For no toppling,
$\overrightarrow{{\tau }_N}+\overrightarrow{{\tau }_{fs}}+\overrightarrow{{\tau }_{mg}}=0$
$\Rightarrow Nx=\mu N\frac{h}{2}$
$\therefore x=\frac{\mu h}{2}\le \frac{a}{2}$
$\Rightarrow \mu \le \frac{a}{h}$

$\Rightarrow$ option (a) and (d) are correct.