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QJEEM22Phdb65: JEE Main 2022 Physics - Class 11 JEEM22Phdb65 Solution: A uniform metal chain of mass m and length 'L' passes over a…

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\mathrm{L}-l ' is hanging on the other side of the pully. At a certain point of time, when l=Lxl=\frac{L}{x} , the acceleration of the chain is g2\frac{g}{2} . The value of x is __________.

JEE Main 2022 (Online) 28th July Evening Shift Physics - Laws of Motion Question 43 English

Multiple Choice Options

  • A 6
  • B 2
  • C 1.5
  • D 4

Step-by-Step Verified Solution

JEE Main 2022 (Online) 28th July Evening Shift Physics - Laws of Motion Question 43 English Explanation



Mass of length l,m1=MLll, m_1=\frac{M}{L} l

Mass of length L−l,m2=ML(L−l)L-l, m_2=\frac{M}{L}(L-l)

Total mass of chain M=m1+m2\mathbf{M}=m_1+m_2

From newton's laws of motion

amp;m2g−m1g=(m2+m1)g2amp;⇒ML(L−l)g−ML(l)g=Mg2amp;⇒L−l−l=L2amp;⇒l=L4\begin{aligned}& m_2 g-m_1 g=\left(m_2+m_1\right) \frac{g}{2} \\\\& \Rightarrow \frac{M}{L}(L-l) g-\frac{M}{L}(l) g=M \frac{g}{2} \\\\& \Rightarrow L-l-l=\frac{L}{2} \\\\& \Rightarrow l=\frac{L}{4}\end{aligned}

Comparing with given equation, l=Lxl=\frac{L}{x} , we get x=4x=4

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