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A uniform metal chain of mass $\mathrm{m}$ and length $\mathrm{ ' L '}$ 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 pully. At a certain point of time, when ${l=\frac{L}{x}}$ , the acceleration of the chain is $\mathrm{\frac{g}{2}}$ . The value of $\mathrm{x}$ is________________.

Option: 1
$6$

Option: 2
$2$

Option: 3
$1.5$

Option: 4
$4$

Answers (1)

best_answer

Let the mass of complete chain be $\mathrm{' m ' }$ and mass of chain of length $\mathrm{ ' \ell '}$ and $\mathrm{ ' L-\ell '}$ be $\mathrm{m_1 \: and \: m_2}$ respectively

$\mathrm{m_1+m_2=m }$

$\mathrm{m_1=\left(\frac{m}{L}\right) \ell}$

$\mathrm{m_2=\left(\frac{m}{L}\right)(L-\ell) }$

$\mathrm{\left(m_2-m_1\right)_{g}=\left(m_2+m_1\right) a }$

$\mathrm{a=\left(\frac{m_2-m_1}{m_2+m_1}\right) g }$

$\mathrm{\frac{g}{2}=\frac{\left ( \frac{m}{L} \right )\left ( L-2\ell \right )}{m}g}$

$\mathrm{\frac{1}{2}=\frac{L-2\ell}{L}}$

$\mathrm{L=2L-4\ell}$

$\mathrm{4\ell=L}$

$\mathrm{\ell=\frac{L}{4}}$

$\mathrm{\therefore x=4}$

Hence 4 is the correct option

Posted by

avinash.dongre

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