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  • 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 the length of the chain that can h

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 the length of the chain that can hang over one edge of the table is

 

Option: 1

20%
 


Option: 2

25%


Option: 3

35%

 


Option: 4

15%


Answers (1)

best_answer

 

 

Maximum Length of Hung Chain -

A uniform chain of length l is placed on the table in such a manner that its l' part is hanging over the edge of the table without sliding.

As \mu=\frac{m_{2}}{m_{1}}=\frac{mass\ hanging\ from\ table}{mass\ on\ table}

The chain will have uniform linear density.

So the ratio of mass and ratio of length for any part of the chain will be equal. 

\mu=\frac{length \ of \ part\ hanging\ from\ table}{length \ of \ part\ \ on\ table}=\frac{l'}{{l-l'}}

l'=\frac{\mu\ l}{(\mu+1)}

Where l= length of chain

l'= chain hanging

(l-l')= chain lying on table

                          

From the expression,

l' = \left ( \frac{\mu }{\mu +1} \right )l=\left ( \frac{0.25}{0.25+1} \right )l             \left [ As\; \mu =0.25 \right ]

\Rightarrow l' = \frac{0.25}{1.25}l=\frac{1}{5}= 20 \ \% \ of \ the \ length \ of \ the \ chain.

Posted by

Nehul

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