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Tension in a String

Find T1 in th...

Question

Find $T_{1}$ in the shown figure. (Assume $g = 10 {m/s}^{2}$ )

220 N

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240 N

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260 N

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280 N

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Solution

The correct option is B $240 N$
Using FBD

For Equilibrium
$\sum F_{x} = 0$
$T_{1} cos 37 = T_{2} cos 53$
$T_{1} \times \frac{4}{5} = T_{2} \times \frac{3}{5}$
$\Rightarrow 4 T_{1} = 3 T_{2}$
$\sum F_{y} = 0$
$T_{1} sin 37 + T_{2} sin 53 = 40 g$
$\frac{3 T_{1} + 4 T_{2}}{5} = 40 g$
putting $T_{2} = 4 T_{1} / 3$
$\Rightarrow 3 T_{1} + \frac{16 T_{1}}{3} = 5 \times 40 g$
$T_{1} = \frac{(5 \times 40 \times 10) 3}{25} = 240 N$

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