In the figure shown, find the tension $T_{1}$ (in $N$ ) in the string. Assume the strings to be inextensible and pulley frictionless.

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 $4 g$
The given arrangement is shown in the below figure.
Consider $2 k g$ and $3 k g$ masses as a system and let the acceleration of the entire system is given by $a$ .

From the FBD of $10 k g$ mass and combined mass of $2 k g$ and $3 k g$ , we get
$\frac{\begin{matrix} 10 g - T = 10 a T - 5 g = 5 a \end{matrix}}{\begin{matrix} 5 g = 15 a a = \frac{g}{3} m / s^{2} \end{matrix}}$
From the FBD of $3 K g$ mass we have

From the FBD of $3 k g$ mass,
$T_{1} - 3 g = 3 a \Rightarrow T_{1} = 3 (g + a) = 3 (g + \frac{g}{3})$
Thus, $T_{1} = 4 g N$

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