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Physics · LAWS OF MOTION
हिन्दीA heavy sphere of mass \( 8\text{ kg} \) is suspended in equilibrium by two light inextensible strings attached to rigid ceiling supports. One string makes an angle of \( 30^\circ \) with the vertical, while the other string makes an angle of \( 60^\circ \) with the vertical. Taking \( g = 10\text{ m/s}^2 \), the tension in the string making an angle of \( 30^\circ \) with the vertical is:
Correct answer · Option 1
\( 40\sqrt{3}\text{ N} \)
Explanation
Let \( T_1 \) be tension at \( 30^\circ \) to vertical and \( T_2 \) at \( 60^\circ \). Horizontal equilibrium: \( T_1 \sin 30^\circ = T_2 \sin 60^\circ \Rightarrow T_2 = \frac{T_1}{\sqrt{3}} \). Vertical equilibrium: \( T_1 \cos 30^\circ + T_2 \cos 60^\circ = mg \Rightarrow T_1 \frac{\sqrt{3}}{2} + (\frac{T_1}{\sqrt{3}}) \frac{1}{2} = 80 \Rightarrow T_1 (\frac{3+1}{2\sqrt{3}}) = 80 \Rightarrow T_1 = 40\sqrt{3}\text{ N} \).
