The boxes of masses 2 kg and 8 kg are connected by a massless string… | JEE Main 2021 (27 Aug, Shift 2)

Q30JEE Main 2021 · 27 AUG · SHIFT 2Medium

Connected Bodies & Pulleys

The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use g = 10 m/s2)

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Answer: (d)

The 8 kg box hangs from a movable pulley held by two string segments, so if it goes down with $a$ , the 2 kg box goes up with $2a$ .
8 kg: $8g - 2T = 8a$ ; 2 kg: $T - 2g = 2(2a) \Rightarrow T = 20 + 4a$
$80 - 40 - 8a = 8a \Rightarrow a = 2.5\text{ m/s}^2$
$s = \tfrac{1}{2}at^2$ : $0.2 = \tfrac{1}{2}(2.5)t^2 \Rightarrow t^2 = 0.16$
$t = 0.4$ s, so the answer is (d).

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