A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitude of tensions and , respectively, are in N): [2025]

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Solution

Q.

A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitude of tensions $T_{1}$ and $T_{2}$ , respectively, are (in N): [2025]

1 $5, 5 \sqrt{3}$

2 $5 \sqrt{3}, 5$

3 $5 \sqrt{3}, 5 \sqrt{3}$

4 5, 5

Ans.
(2)

$T_{1} \sin 60 ° + T_{2} \sin 30 ° = m g$ ... (i)

$T_{1} \cos 60 ° = T_{2} \cos 30 °$ ... (ii)

$T_{1} = \sqrt{3} T_{2}$ ... (iii)

From (i) and (iii)

$\sqrt{3} T_{2} \times \frac{\sqrt{3}}{2} + \frac{T_{2}}{2} = m g$

$T_{2} = \frac{m g}{2} = 5 N$

and $T_{1} = \frac{\sqrt{3} m g}{2} = 5 \sqrt{3} N$

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