Question

A body of mass 1kg is suspended with the help of two strings making angles as shown in the figure. Magnitude of tensions $ T_1 $ and $ T_2 $, respectively, are (in N):

• A. 5, \( 5\sqrt{3} \)
• B. \( 5\sqrt{3} \), 5
• C. \( 5\sqrt{3} \), \( 5\sqrt{3} \)
• D. 5, 5

Hint:

When dealing with problems of forces in equilibrium, remember to resolve the forces into vertical and horizontal components and apply the equilibrium conditions.

Answer 1

The Correct Option is B

Given that the body is in equilibrium, we can resolve the forces in the vertical and horizontal directions. 
The weight of the body is \( mg = 1 \times 9.8 = 9.8 \, \text{N} \). For the vertical direction: \[ T_1 \sin 30^\circ + T_2 \sin 30^\circ = mg \] For the horizontal direction: \[ T_1 \cos 30^\circ = T_2 \cos 30^\circ \] Thus: \[ T_1 = T_2 \] Now, solving for the tensions using the vertical direction equation: \[ T_1 \sin 30^\circ + T_1 \sin 30^\circ = 9.8 \, \text{N} \] \[ 2T_1 \sin 30^\circ = 9.8 \] \[ 2T_1 \times \frac{1}{2} = 9.8 \] \[ T_1 = 5 \, \text{N}, \, T_2 = 5\sqrt{3} \, \text{N} \] Thus, the correct answer is: \( T_1 = 5 \), \(\text{N} \, T_2 = 5\sqrt{3} \), \(\text{N} \)