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Intensity Explanation in YDSE

In the system...

Question

In the system of pulleys shown, what should be the value of $m_{1}$ such that $100 g$ remain at rest with respect to earth.

180 g

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160 g

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100 g

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200 g

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Solution

The correct option is B $160 g$
$\begin{matrix} A s 100 g m b l o c k i s a t r e s t S o, T - 100 g = 0. T = 100 g . N o w, i n 200 g m b l o c k 200 g - T = 200 a . p u t t i n g v a l u e o f T, w e g e t a = 5 m / s^{2} N o w, a t m_{1} b l o c k . a c c e l e r a t i o n w i l l b e \frac{0 + 5}{2} = 2.5 N o w, 2 T - m_{1} g = m_{1} a p u t t i n g v a l u e o f T a n d a w e g e t m_{1} = 160 g \end{matrix}$
hence,
option $(B)$ is correct answer.

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