Question

A uniform chain of length 2m is kept on a table such that a length of 60cm hangs freely from the edge of the table. The total mass of the chain is $4kg$. What is the work done in pulling the entire chain on the table?
A.$12J$
B.$3.6J$
C.$7.2J$
D.$1200J$

Answer 1

The distance of the centre of mass of the chain from the table is given by the half of the length of the chain that hangs freely from edge of the table.
For finding the work done in pulling the entire chain on the table, we will use the formula-
Work done$= mgh$, Where W, m, and h have their usual meaning.

Complete step by step solution:
The total mass of the chain is given = $M = 4kg$
Chain length = $L = 2m$
Length of the chain that hangs freely from edge of the table = $l = 60cm = 0.6m$
Mass of the chain hanging freely from the table = $M \times \dfrac{l}{L}$
Mass of the chain hanging freely from the table = $4 \times \dfrac{{0.6}}{2}$
Mass of the chain hanging freely from the table = $1.2kg$
The distance of the centre of mass of the chain from the table is given by the half of the length of the chain that hangs freely from the edge of the table.
So, Distance of centre of mass of chain from the table =$\dfrac{l}{2}$
Distance of centre of mass of chain from the table =$\dfrac{{0.6}}{2}$
Distance of centre of mass of chain from the table =$0.3m$

Thus the work done in pulling the complete chain = $mgh$
Where, $m =$ Mass of the chain hanging freely from the table
$g =$Acceleration due to gravity on the surface of the earth
$h =$ Distance of centre of mass of chain from the table
The work done in pulling the complete chain = $1.2 \times 9.8 \times 0.3$
The work done in pulling the complete chain = $3.528 \approx 3.6J$

Hence option (B) is the correct answer.

Note: Students make a lot of mistakes while calculating the mass and centre of mass of the hanging part so be careful while solving that. When work is done on the object, the object gains energy and when work is done by the object, the object loses its energy.