All surfaces shown in figure are assumed to be frictionless and the… | JEE Main 2024 (30 Jan, Shift 1)

Q16JEE Main 2024 · 30 JAN · SHIFT 1Medium

Connected Bodies & Pulleys

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass $2\text{ kg}$ is:

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Answer: (d)

The 4 kg block hangs from a movable pulley (two segments), so if the 2 kg block moves up the incline with $2a$ , the 4 kg block moves down with $a$ .
4 kg: $4g - 2T = 4a$
2 kg: $T - 2g\sin 30^\circ = 2(2a) \Rightarrow T = g + 4a$
$4g - 2g - 8a = 4a \Rightarrow a = \dfrac{g}{6}$
Acceleration of 2 kg block $= 2a = \dfrac{g}{3}$ , so the answer is (d).

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