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Tension in a String

Three blocks ...

Question

Three blocks $A$ , $B$ and $C$ weighing $1 k g, 8 k g$ and $27 k g$ respectively are connected as shown in the figure, with an inextensible string and are moving on a smooth surface. If tension $T_{3}$ is equal to $36 N$ , then tension $T_{2}$ is

18 N

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9 N

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3.375 N

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1.25 N

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Solution

The correct option is B $9 N$
Consider all the blocks connected with inextensible strings as a system.
FBD of the system will be:

From second law, net acceleration of the system,
$a_{n e t} = \frac{F_{n e t}}{m_{t o t a l}} = \frac{36}{1 + 8 + 27} = 1 m / s^{2}$

Now FBD of $27 k g$ block will be

$36 - T_{2} = m a_{n e t} = 27 \times 1$
$\Rightarrow T_{2} = 9 N$

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Three blocks A, B and C weighing 1 kg,8 kg and 27 kg respectively are connected as shown in the figure, with an inextensible string and are moving on a smooth surface. If tension T3 is equal to 36 N, then tension T2 is

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