Laws of Motion - Result Question 51
51. 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) $15 %$
[1991]
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Answer:
Correct Answer: 51. (a)
Solution:
- (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
Now, $\mu(l-x) \rho g=x \rho g$ or $\mu(l-x)=x$
or $\mu l=(\mu+1) x$ or $x=\mu l /(\mu+1)$ $\therefore \quad x=\frac{0.25 l}{(0.25+1)}=\frac{0.25 l}{1.25}=0.2 l$
$\frac{x}{l}=0.2 \Rightarrow \frac{x}{\ell} \times 100=20 %$
