In the arrangement shown in figure a _ 1 , a _ 2 , a _ 3 and a _ 4...

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?

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 _

Options

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

Correct answer

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

Step-by-step solution

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

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 _

$∑ \overset{\to}{T} \cdot \overset{\to}{a} = 0$

$⇒ \left(4T\right){a}_{1} + \left(2T\right){a}_{2} + T{a}_{3} + T{a}_{4} = 0$

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

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