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Tension in a String

Three blocks ...

Question

Three blocks are connected by a light inextensible string as shown in the figure and placed on a horizontal table. If $m_{1} = 10 k g, m_{2} = 20 k g$ and $m_{3} = 30 k g$ , find the tension $T_{1}$ given that $T_{3} = 60 N$

A

zero

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B

45 N

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C

30 N

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D

10 N

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Solution

The correct option is D $10 N$
The FBD of the mass $m_{1}$ is as shown

Let $a$ be common the acceleration of the system, which is given by
$a = \frac{(Supporting Force-Opposing Force)}{Total mass} = \frac{T_{3}}{m_{1} + m_{2} + m_{3}}$
$= \frac{60}{10 + 20 + 30} = 1 m / s^{2}$
From the FBD of $m_{1}$ , we have
$T_{1} = m_{1} a = 10 \times 1 = 10 N$

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