Question

A metal chain of mass $2kg$ and length $90cm$ over hangs a table with $60cm$ on the table. How much work needs to be done to put the hanging part of the chain back on the table? $($ Let $g=10m/s^2)$

• A. 2 J
• B. 10 J
• C. 1 J
• D. 3 J

Answer 1

Answer: (C)

Given, mass of metal chain, $m=2kg$,
Total length of chain, $l=90cm=0.9m$,
Hanging length of chain, $l^{{}^{\prime }}=(90-60)cm$
$=30cm=0.3m$
The distance of centre of gravity of hanging length from the table,
$l_c=\frac{l^{{}^{\prime }}}{2}=\frac{0.3}{2}=0.15m$
Mass of the hanging part of chain,
$m^{{}^{\prime }}=\frac{0.30}{0.90}\times 2$
$m^{{}^{\prime }}=\frac{2}{3}kg$
$\therefore$ Work needed to put hanging part of the chain back on the table,
$W=m^{{}^{\prime }}g{l}_c$
$=\frac{2}{3}\times 10\times 0.15=1J\left(\because g=10m/s^2\right)$