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?

Concept:
For an inextensible string,

$$\sum_{ }^{ }T⃗⋅a⃗=0$$

i.e., sum of components of accelerations along tension = 0.

Applying to system (counting segments):

$$-4Ta_1-2Ta_2-Ta_3-Ta_4=0$$

Cancel T:

$$-4a_1-2a_2-a_3-a_4=0$$

Final Answer:

$$-4a_1-2a_2-a_3-a_4=0$$

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