In the figure M₁=4M₂The pulleys are smooth and light. At time t = 0, the system is at rest. If
the system is released, the acceleration of mass M₁is

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g/2

g/8

g/4

answer is C.

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Detailed Solution

$M_{1} g - 2 T = M_{1} a \to (1) T - M_{2} g = M_{2} (2 a) \to (2) s o l v i n g (1) & (2) (1) \Rightarrow M_{1} g - 2 T = M_{1} a 2 \times (2) \Rightarrow 2 T - 2 M_{2} g = 2 M_{2} (2 a) M_{1} g - 2 M_{2} g = M_{1} a + 4 M_{2} a ∵ M_{1} = 4 M_{2} 4 M_{2} g - 2 M_{2} g = 4 M_{2} a + 4 M_{2} a 2 M_{2} g = 8 M_{2} a a = \frac{g}{4}$