Question

A uniform chain ABC of mass $m$ and length $l$ overhangs a table with its two third part on the table.
What is the potential energy of chain-earth system assuming the base of the table as zero potential energy level?

• A. $\frac{mgl}{18}$
• B. $\frac{4mgl}{18}$
• C. $\frac{-mgl}{18}$
• D. $\frac{-4mgl}{18}$

Answer 1

The correct option is A $\frac{mgl}{18}$

Mass of the hanging portion $=\frac{m}{l}\times \frac{l}{3}=\frac{m}{3}$

Center of mass of the hanging portion from the top of the level$=\frac{l}{6}$

Work done= increase in potential energy $=\frac{m}{3}\times g\times \frac{l}{6}=\frac{mgl}{18}$