JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Laws of Motion

In the arrangement shown in figure

a_{1}, a_{2}, a_{3}

and

a_{4}

are the accelerations of masses

m_{1}, m_{2}, m_{3}

and

m_{4}

respectively. Which of the following relation is true for this arrangement?

(A) $4 a_{1} + 2 a_{2} + a_{3} + a_{4} = 0$ ✓ Correct
(B) $a_{1} + 4 a_{2} + 3 a_{3} + a_{4} = 0$
(C) $a_{1} + 4 a_{2} + 3 a_{3} + 2 a_{4} = 0$
(D) $2 a_{1} + 2 a_{2} + 3 a_{3} + a_{4} = 0$

Answer: (A)

Solution

Using the constraint relation for the pulley system, the sum of the products of tension and acceleration along each string segment must be zero:

\sum T \cdot a = 0

. For this arrangement, the constraint gives

- 4 T a_{1} - 2 T a_{2} - T a_{3} - T a_{4} = 0

. Dividing by

- T

, we obtain

4 a_{1} + 2 a_{2} + a_{3} + a_{4} = 0

JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Single correct option

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