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Pulley

In the figure...

Question

In the figure shown, find the tension $T_{1}$ in the string. Take $g = 10 m / s^{2}$

2 g

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3 g

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2.5 g

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4 g

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Solution

The correct option is D $4 g$
Since $10 k g > (2 + 3) k g$ , the $10 k g$ mass will move downward.

Acceleration of the system
$a = \frac{Supporting mass - Opposing mass}{Total mass}$
$= \frac{10 g - 5 g}{15} = \frac{g}{3} m / s^{2}$

FBD of $3 k g$ mass :

$T_{1} - 3 g = 3 a$
$\Rightarrow T_{1} = 3 (\frac{g}{3}) + 3 g = 4 g N$

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