Question

A uniform chain of length $2m$ is kept on a table such that a length of $50cm$ hangs freely from the edge of the table. The total mass of the chain is $5kg$. What is the work done in pulling the entire chain on the table. (in J)

• A. $7.2$
• B. $3$
  
• C. $4.6$
  
• D. $12$
  

Answer 1

The correct option is B $3$

Mass per unit length of chain $=M/L=5/2=2.5kg/m$

Work done in pulling the chain of length $dx=dW=mgx=\left(2.5dx\right)\left(10\right)x$

Inregrating both sides with proper limits $x=0m$ $to$ $x=0.5m$, we get

$\Rightarrow W={\int }_0^{0.5}\left(25x\right)dx$

$\Rightarrow W=12.5({0.5}^2-0^2)=3.125J\approx 3J$

Hence correct answer is option $B$