A uniform chain of length 
and mass 
is lying on a smooth table and one–third of its length is hanging vertically down over the edge of the table. If 
is the acceleration due to gravity, the work required to pull the hanging part on to the table is
a)
b)
c)
d)
A uniform chain of length and mass is lying on a smooth table and one–third of its length is hanging vertically down over the edge of the table. If is the acceleration due to gravity, the work required to pull the hanging part on to the table is
a)
b)
c)
d)
Question ID - 100656 | SaraNextGen Top Answer
A uniform chain of length and mass is lying on a smooth table and one–third of its length is hanging vertically down over the edge of the table. If is the acceleration due to gravity, the work required to pull the hanging part on to the table is
a)
b)
c)
d)
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A uniform chain of length |
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a) |
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b) |
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c) |
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d) |
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(d)
Method I:
The hanging part of the chain which is to be pulled can be considered as a point mass situated at the centre of the hanging part. The equivalent diagram is drawn The work done in bringing the mass up will be equal to the change in potential energy of the mass
Change in potential energy
.png)
Method II:
The mass per unit of the chain
Let us consider a finitesimally small length of the chain 
at a distance 
from the bottom. To move 
to the top, a force equal to the weight of chain 
will have to be applied upwards
.png)
Weight of chain of length
Small amount of work done in moving 
to the top
The total amount of work done in moving the one-third length of the hanging chain on the table will be
