In the arrangement shown in figure a₁,a₂, a₃ and a₄are the accelerations of masses m₁,m₂,m₃ and m₄ respectively. Which of the following relation is true for this arrangement?

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

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

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

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

answer is A.

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Detailed Solution

Using costraint
$\begin{array}{l} \sum \vec{T} \cdot \vec{a} = 0 \\ - 4 {Ta}_{1} - 2 {Ta}_{2} - {Ta}_{3} - T a_{4} = 0 \\ 4 a_{1} + 2 a_{2} + a_{3} + a_{4} = 0 \end{array}$

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