Question

A chain is placed on a rough table, partially hanging, as shown in the figure. The coefficient of static friction between the chain and the table is $\mu =\mathrm{0.4.}$ If the maximum possible length of the hanging part is $x$ and the length of the chain is $L$ , then what is the value of $\frac{L}{x}$ ?

Answer 1

Answer: 3.5

If $x=$ length suspended
$m_1=\lambda x$ (mass of hanging part)
$m_2=\lambda (L-x)$ (mass of the part kept on the table)
Then for balance,
$m_{1}g={\mu }_s{m}_{2}g$
$\lambda x=0.4\lambda (L-x)$
$x=0.4L-0.4x$
$1.4x=0.4L$
$\left(\frac{L}{x}\right)=\frac{1.4}{0.4}=3.5$