Question 95 of 210

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$4{a}_{1}+2{a}_{2}+{a}_{3}+{a}_{4}=0$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$2{a}_{1}+2{a}_{2}+3{a}_{3}+{a}_{4}=0$

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Answer: (A) $4{a}_{1}+2{a}_{2}+{a}_{3}+{a}_{4}=0$

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

$\sum \vec{T}\cdot \vec{a}=0$
$\Rightarrow \left(4T\right){a}_{1}+\left(2T\right){a}_{2}+T{a}_{3}+T{a}_{4}=0$
$\Rightarrow 4{a}_{1}+2{a}_{2}+{a}_{3}+{a}_{4}=0$