Question

A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table?

• A. 7.2 J
• B. 3.6 J
• C. 120 J
• D. 400 J

Answer 1

The correct option is B 3.6 J

Given,

$m=4kg$

$l=2m$

$g=10m/s$

The work is done in lifting a small portion, $dw=dm.gx$

$W=\int dw=\int \frac{m}{l}dx.gx$

$W=\frac{mg}{l}{\int }_0^{h}xdx$

$W=\frac{mg}{l}[\frac{x^2}{2}{]}_0^h$

$W=\frac{4\times 10}{2}\frac{0.6\times 0.6}{2}$

$W=3.6J$

The correct option is B.