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Q.

A ball of mass 1 kg hangs in equilibrium from two strings OA and OB as shown in figure. What are the tensions in strings OA and OB? ( Take g=10 m/s² )

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a

$5 N, 5 N$

b

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

c

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

d

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

answer is C.

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Detailed Solution

Apply Lami's Theorem at O

$\frac{T_{1}}{\sin 150^{\circ}} = \frac{T_{2}}{\sin 120^{\circ}} = \frac{10}{\sin 90^{\circ}} = \frac{10}{1} = 10 ∴ T_{1} = 10 \sin 150^{\circ} = 10 \times \frac{1}{2} = 5 N T_{2} = 10 \sin 120^{\circ} = 10 \times \frac{\sqrt{3}}{2} = 5 \sqrt{3} N$

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