Question

A chain lies on a rough horizontal table. It starts sliding when one-fourth of its length hangs over the edge of the table. The coefficient of static friction between the chain and the surface of the table is:

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

The correct option is B $\frac{1}{3}$

Let the length of the uniform chain be $l$ and mass be $m$.

Let the friction coefficient be $\mu$.

The chain starts sliding when one-fourth of its length hangs over the edge of the table.

Hence mass of one-fourth of its length is $\frac{m}{4}$.

Frictional force $F$ acting on chain is due to the $\frac{3l}{4}$ length of chain.

$F=\mu \times \frac{3mg}{4}$

On the verge of sliding,

$F=$ weight of hanging portion of chain

$F=\frac{mg}{4}$

$\mu \times \frac{3mg}{4}=\frac{mg}{4}$

$\mu =\frac{1}{3}$