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Tension in a String

If F= 120 N w...

Question

If $F = 120 N$ which is parallel to the inclined plane, find the tension $T_{2}$ in string. $(g = 10 m / s^{2})$

15 N

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30 N

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45 N

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60 N

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Solution

The correct option is D $60 N$
Considering $(2 k g + 4 k g + 6 k g)$ as a system, the FBD of the $12 k g$ body is

As $120 N > 12 g sin 37^{\circ} (= 72 N)$ , the system will accelerate up the plane.
Hence $a = \frac{120 - 72}{12} = 4 m / s^{2}$
Hence for calculating $T_{2}$ , consider the FBD of $(2 k g + 4 k g)$

$T_{2} - 6 g sin 37^{\circ} = m a = 6 \times 4$
$\Rightarrow T_{2} = 60 N$

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