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Question

A chain of mass m and length l is placed on a table with one-sixth of it hanging freely from the table edge. The amount of work done to pull the chain on to the table is

A
mgl4
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B
mgl6
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C
mgl72
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D
mgl36
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Solution

The correct option is C mgl72

Given, the total mass of chain =m

Length of chain =l

So, mass per unit length is (λ=m/l)

If we consider a small element dx at a distance 'x' from the table, then the small mass element dm is given as:

dm=mldx

So, work done against gravity in lifting the small mass element dm through x distance is :

dW=dmgx=(m/l)gxdx

Now, total work done is obtained by integrating dW from limits x=0 to x=l6 as one-sixth of the chain hangs from table.

W0dW=mglx(dx)=mgll60x dx

W=mg2l(l6)2=mgl72


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