A uniform metal chain of mass m and length 'L' passes over a massless… | JEE Main 2022 (28 Jul, Shift 2)

Q23JEE Main 2022 · 28 JUL · SHIFT 2Medium

Connected Bodies & Pulleys

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' 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 __________.

Show answer and solution

Answer: (d)

Mass per length $\lambda = \frac{m}{L}$ . Net driving force $= \lambda g[(L - l) - l]$ , moving mass $= m$ .
$a = \dfrac{g(L - 2l)}{L} = \dfrac{g}{2} \Rightarrow L - 2l = \dfrac{L}{2}$
$l = \dfrac{L}{4} \Rightarrow x = 4$ , so the answer is (d).

Report a mistake

More questions on Connected Bodies & Pulleys

A system of 10 balls each of mass 2 kg are connected via massless and unstretchable…JEE Main 2022 (26 Jun, Shift 2)
Two masses M₁ and M₂ are tied together at the two ends of a light inextensible string…JEE Main 2022 (26 Jul, Shift 2)
Three masses M = 100 kg, m₁ = 10 kg and m₂ = 20 kg are arranged in a system as shown in…JEE Main 2022 (26 Jul, Shift 1)
A hanging mass M is connected to a four times bigger mass by using a string-pulley…JEE Main 2022 (28 Jun, Shift 1)
In the arrangement shown in figure a1, a2, a3 and a4 are the accelerations of masses m1…JEE Main 2022 (26 Jun, Shift 2)
Two masses A and B, each of mass M are fixed together by a massless spring. A force acts…JEE Main 2021 (26 Feb, Shift 2)
The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth…JEE Main 2021 (27 Aug, Shift 2)
A block of mass m slides on the wooden wedge, which in turn slides backward on the…JEE Main 2021 (1 Sep, Shift 2)

Connected Bodies & Pulleys question from JEE Main 2022 (28 Jul, Shift 2)

More questions on Connected Bodies & Pulleys