# 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 :- 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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(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

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

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

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