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Applying NLM along 3 Axis

Three blocks ...

Question

Three blocks are connected as shown in the figure, on a horizontal frictionless table and pulled to the right with a force of $60 N$ . if $M_{1} = 10 k g$ , $M_{2} = 20 k g$ and $M_{3} = 30 k g$ then the value of $T_{2}$ :

A

90 N

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B

45 N

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C

60 N

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D

30 N

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Solution

The correct option is C $30 N$
Let $a$ be the acceleration of the system.
$T_{1} = M_{1} a$ .....(1)
$T_{2} - T_{1} = M_{2} a$ ....(2)
$F - T_{2} = M_{3} a$ ......(3)
Adding (1), (2) and (3) we get
$(M_{1} + M_{2} + M_{3}) a = F$
or $(10 + 20 + 30) a = 60 \Rightarrow a = 1 m / s^{2}$
Now , $T_{2} = (M_{1} + M_{2}) a = (10 + 20) (1) = 30 N$

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