Question

A heavy uniform chain lies on a horizontal tabletop. If the coefficient of friction between the chain and the table surface is $0.25$ , then the maximum fraction 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

Answer: (A)

The force of friction on the chain lying on the table should be equal to the weight of the hanging chain. Let
$\rho =$ mass per unit length of the chain
$\mu =$ coefficient of friction
$l=$ length of the total chain
$x=$ length of hanging chain
$$\begin{gathered} Now,\mu (l-x)\rho g=x\rho gor\mu (l-x)=x \\ \Rightarrow \mu l=(\mu +1)xorx=\frac{\mu l}{(\mu +1)} \\ \therefore x=\frac{0.25l}{(0.25+1)}=\frac{0.25l}{1.25}=0.2l \\ \therefore \frac{x}{l}=0.2=20\% \end{gathered}$$