Question

A heavy uniform chain lies on horizontal table top. 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

The correct option is A 20%

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
Now, $\mu (l-x)\rho g=x\rho g$ or $\mu (l-x)=x$
or $\mu l=(\mu +1)x$ or $x=\frac{\mu l}{(\mu +1)}$
$\therefore x=\frac{0.25l}{(0.25+1)}=\frac{0.25l}{1.25}=0.2l$
$\frac{x}{l}=0.2$