Question

A heavy uniform chain lies on a horizontal top of table. If the coefficient of friction between the chain and the table is $0.25$ then the maximum percentage of the length of the chain that can hang over one edge of the table is:

• A. $20$ %
• B. $25$ %
• C. $35$ %
• D. $15$ %

Answer 1

The correct option is A $20$ %

Let the length of total chain be $l$

The part which is lying on the table be $x$ and lying outside be $y$

In equilibrium , the frictional force must balance the tension force

Let us take $t$ as weight per unit length and $n$ as coefficient of friction

We get $ntx=ty$

$\Rightarrow nx=y$

Here we need to find $\frac{y}{l}$

$\Rightarrow \frac{y}{l}=\frac{y}{x+y}=\frac{n}{n+1}$

Given $n=0.25$

So we get $\frac{y}{l}=\frac{0.25}{1+0.25}=\frac{1}{5}$

Therefore the maximum percentage of chain hanging is $\frac{1}{5}\times 100=20$%

Therefore option $A$ is correct