Question

A uniform metal chain of mass $m$ and length '$L$' passes over a massless and frictionless pulley. It is released from rest with a part of its length ' $l$ ' is hanging on one side and rest of its length ' $L -l$ ' is hanging on the other side of the pulley. At a certain point of time, when $l=\frac{ L }{ x }$, the acceleration of the chain is $\frac{ g }{2}$. The value of $x$ is $\ldots \ldots . .$.

• A. 6
• B. 2
• C. 1.5
• D. 4

Answer 1

Answer: (D)

$a =\frac{\left( m _2- m _1\right)}{\left( m _2+ m _1\right)} g $
$ \frac{ g }{2}=\frac{(\lambda( L -\ell)-\lambda \ell) g }{\lambda L } $
$\Rightarrow L =\frac{ L }{4}=\frac{ L }{ x } $
$ x =4$