Question

A uniform metal chain is placed on a rough table such that one end of the chain hangs down over the edge of the table. When one-third of its length hangs over the edge, the chain starts sliding. Then, the coefficient of static friction is

• A. $3/4$
• B. $1/4$
• C. $2/3$
• D. $1/2$

Answer 1

The correct option is D

$1/2$

Step 1: Given data

Length of the chain $=l$

Mass of the chain $=m$

One-third of its length hangs over the edge $=1/3$

Mass distributed along the length $=m/3$

The length of the chain on the table $=2l/3$

Step 2: To find the coefficient of static friction

Writing the equation for the force balance along the chain

$mg-2mg\mu =0$

$$\begin{gathered} mg=2mg\mu \\ \mu =1/2 \end{gathered}$$

Hence the coefficient of static friction $\mu =1/2$

Therefore the correct answer is Option D