question_answer

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)  1200 J

Correct Answer: B

Solution :

Fraction of length of the chain hanging from the table \[=\frac{1}{n}=\frac{60cm}{200\,cm}=\frac{3}{10}\Rightarrow n=\frac{10}{3}\] Work done in pulling the chain on the table as shown in the figure, \[W=\frac{mg}{n}\left( \frac{\ell }{2n} \right)=\frac{mgl}{2{{n}^{2}}}=\frac{4\times 10\times 2}{2\times {{(10/3)}^{2}}}=3.6\,J.\] Hence, the correction option is [b].