Question bank/JEE Main/Physics

In the system shown in figure mA = 4m, mB = 3m and mC = 8m.
Friction is absent everywhere. String is light and inextensible. If the
system is released from rest find the acceleration of block B

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$T = m_{B}b$[Newtons II law for B in horizontal direction]
$T = \left\lbrack m_{A} + m_{e} \right\rbrack c$ I law for A
and C in horizontal direction]
$m_{A}g - T = m_{A}a$ [Newton's II law for A in vertical direction].
$\frac{m_{A}g - T}{m_{A}} = \frac{T}{m_{B}} + \frac{T}{m_{A} + m_{C}}$
$\frac{4mg - T}{4m} = \frac{T}{3m} + \frac{T}{12m} \Rightarrow T = \frac{3mg}{2} \Rightarrow b = \frac{g}{2}$

Source: Grass-G / P-06 Physics paper 14 October.docx