Question

A homogeneous block of mass $m$, width $b$ and height $h$ is resting on a rough horizontal surface. A horizontal force $F$ is applied to it, which makes it to move with a constant velocity. The coefficient of friction between block and surface is $\mu$. Find the greatest height at which force $F$ may be applied to slide the block without tipping over.

• A. $\frac{b}{2\mu }$
• B. $\frac{2b}{\mu }$
• C. $\frac{b}{\mu }$
• D. $\frac{2\sqrt{2}b}{\mu }$

Answer 1

Answer: (A)

$\frac{b}{2\mu }$

To not topple the torque on it must be balanced.

Now,

$F\left(x\right)=mg\left(\frac{b}{2}\right)x=\frac{mgb}{2F}$

On balancing force

$\mu N=F\mu mg=F$

So,

$x=\frac{mgb}{2\mu mg}x=\frac{b}{2\mu }$