Q 11-04-092JEE MainJEE Main 2024 (30 Jan, Shift 1)Medium
All surfaces shown in the 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:
Answer: (B) $\dfrac g3$
The 4 kg block hangs from a movable pulley, so if the 2 kg block moves up the incline with acceleration $a$, the 4 kg block goes down with $a/2$.
2 kg block: $T - 2g\sin30^\circ = 2a \Rightarrow T = g + 2a$
4 kg block (two string segments hold the pulley): $4g - 2T = 4\cdot\dfrac a2 = 2a$
Substituting: $4g - 2g - 4a = 2a \Rightarrow a = \dfrac g3$
Solution by Sreeraj P, M.Sc Physics