Question

A heavy uniform chain lies on a horizontal table top. If the coefficient of friction between the chain and the table surface is $0.25$, then the maximum fraction of length of chain that can overhang on the edge of the table is

• A. $0.20$
• B. $0.35$
• C. $0.25$
• D. $0.15$

Answer 1

The correct option is A $0.20$

The given situation can be considered as shown

Let $x$ be the length of the chain hanging, $L$ be the total length of the chain and mass of total chain be $m$
$\therefore$ mass of $x$ length of the chain will be $xm$ and the mass of $(L-x)$ length of the chain will be $(L-x)m$
So, FBD can be considered as

From the FBD we get
$\Rightarrow T=xmg$
and, $N=(L-x)mg$
Also, $T=f=\mu N$
$\Rightarrow T=0.25(L-x)mg$
$\Rightarrow xmg=0.25(L-x)mg$
$\Rightarrow L-x=4x$
$\Rightarrow x=\frac{L}{5}$
Thus, fraction of chain that can hung is $\frac{x}{L}=\frac{L/5}{L}=0.2$