Question

A uniform metal chain of mass m and length ‘$L$’ passes over a massless and frictionless pully. 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 pully. At a certain point of time, when $l = L/x$, the acceleration of the chain is $g/2$. The value of $x$ is ______.

• A. 6
• B. 2
• C. 1.5
• D. 4

Answer 1

Answer: (D)

4

Answer 2

$a = \frac{(m_2 - m_1)}{(m_2 + m_1)}g$ ⇒ $\frac{g}{2}$ = $\frac{(λ(L - l) - λl)g}{λL}$

⇒ $L = \frac{L}{4} = \frac{L}{x}$

∴ $x = 4$