In the arrangement shown in figure a1, a2, a3 and a4 are the… | JEE Main 2022 (26 Jun, Shift 2)

Q28JEE Main 2022 · 26 JUN · SHIFT 2Difficult

Connected Bodies & Pulleys

In the arrangement shown in figure a1, a2, a3 and a4 are the accelerations of masses m1, m2, m3 and m4 respectively. Which of the following relation is true for this arrangement?

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Answer: (a)

Measure positions downward from the fixed pulley; let $P_2$ , $P_3$ be the two movable pulleys.
String over fixed pulley: $a_1 + a_{P2} = 0 \Rightarrow a_{P2} = -a_1$
String over $P_2$ : $a_2 + a_{P3} = 2a_{P2} \Rightarrow a_{P3} = -2a_1 - a_2$
String over $P_3$ : $a_3 + a_4 = 2a_{P3} = -4a_1 - 2a_2$
$4a_1 + 2a_2 + a_3 + a_4 = 0$ , so the answer is (a).

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