A uniform metal chain of mass m and length L passes over a massless...

According to the information given in the question, the part of the chain that envelopes the pulley is very small. Therefore, the acceleration of the chain can be written as,

$a = \dfrac{\left({m}_{2} - {m}_{1}\right)}{\left({m}_{2} + {m}_{1}\right)}g$

Since $a = \dfrac{g}{2}$

$\dfrac{g}{2} = \dfrac{\left({m}_{2} - {m}_{1}\right)}{\left({m}_{2} + {m}_{1}\right)}g ⇒ \dfrac{g}{2} = \dfrac{\left(L - l\right) - l}{L}g ⇒ l = \dfrac{L}{4} = \dfrac{L}{x}$

$⇒ x = 4$