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Question: A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is han...

A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is –

A

MgL

B

MgL/3

C

MgL/9

D

MgL/18

Answer

MgL/18

Explanation

Solution

Mass of hanging portion is (one-third) and centre of mass c, is at a distance h =below the table top.

Therefore, the required work done is,

W = mgh =MgL18\frac { \mathrm { MgL } } { 18 }