First slide

Concept of potential energy

Question

A man places a chain of mass m and length l on a table slowly. Initially, the lower end of the chain just touches the table. The man brings down the chain by length l/2. Work done by the man in this process is

Moderate

A

$- mg \frac{l}{2}$
B

$- \frac{mgl}{4}$
C

$\frac{- 3 mgl}{8}$
D

$- \frac{mgl}{8}$

Solution

The work done by the man is negative of the magnitude of decrease in potential energy of the chain. (L= l)
$\begin{array}{l} ΔU = mg \frac{l}{2} - \frac{m}{2} g \frac{l}{4} = 3 mg \frac{l}{8} \\ W = - \frac{3 mgl}{8} \end{array}$

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