Q62 / 90 · JEE Main 2022 (26 Jun Shift 2) · Physics

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?

Solution

The figure shows the tension acting on each string in the system.

$\sum \vec{T} \cdot \vec{a} = 0$

$\Rightarrow (4 T) a_{1} + (2 T) a_{2} + T a_{3} + T a_{4} = 0$

$\Rightarrow 4 a_{1} + 2 a_{2} + a_{3} + a_{4} = 0$

Hence, the correct answer is option: 'A'.