JEE MAIN - Physics (2022 - 28th July Evening Shift - No. 4)
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 '$$\mathrm{L}-l$$' 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 $$\frac{g}{2}$$. The value of x is __________.
_28th_July_Evening_Shift_en_4_1.png)
6
2
1.5
4
Explanation
_28th_July_Evening_Shift_en_4_2.png)
Mass of length $l, m_1=\frac{M}{L} l$
Mass of length $L-l, m_2=\frac{M}{L}(L-l)$
Total mass of chain $\mathbf{M}=m_1+m_2$
From newton's laws of motion
$$ \begin{aligned} & m_2 g-m_1 g=\left(m_2+m_1\right) \frac{g}{2} \\\\ & \Rightarrow \frac{M}{L}(L-l) g-\frac{M}{L}(l) g=M \frac{g}{2} \\\\ & \Rightarrow L-l-l=\frac{L}{2} \\\\ & \Rightarrow l=\frac{L}{4} \end{aligned} $$
Comparing with given equation, $l=\frac{L}{x}$, we get $x=4$
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