Question

There is a chain of length $6\text{m}$ and coefficient of friction $\frac{1}{2}$. What will be the maximum length of chain which can be held outside the table without sliding?

• A. $2\text{m}$
• B. $4\text{m}$
• C. $3\text{m}$
• D. $1\text{m}$

Answer 1

The correct option is A $2\text{m}$

Let $y$ be the suspended length
Mass per unit length of chain $=\frac{M}{6}$
Mass of the suspended part $=\frac{M}{6}y$
For equilibrium of chain, the weight of suspended part must be balanced by force of fricion on the portion on the table.
$\mu N=\frac{M}{6}yg$
$\mu \frac{M(6-y)g}{6}=\frac{M}{6}yg$
$\frac{1}{2}(6-y)=y\Rightarrow (6-y)=2y$
$3y=6\Rightarrow y=2\text{m}$