Laws of Motion - Result Question 51

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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

======= ####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

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/laws-of-motion/laws-of-motion—result-question-51.md (a) $20 %$

(b) $25 %$

(c) $35 %$

(d) $15 %$

[1991]

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Answer:

Correct Answer: 51. (a)

Solution:

  1. (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 $x=\mu l /(\mu+1)$ $\therefore \quad x=\frac{0.25 l}{(0.25+1)}=\frac{0.25 l}{1.25}=0.2 l$

$\frac{x}{l}=0.2 \Rightarrow \frac{x}{\ell} \times 100=20 %$