A body of mass m is suspended by two strings making angles θ1 and θ2 with the horizontal ceiling with tensions T1 and T2 simultaneously. ​

Question

A body of mass m is suspended by two strings making angles \(\theta _1\) and \(\theta _2\) with the horizontal ceiling with tensions \(T_1\) and \(T_2\) simultaneously. \(T_1\) and \(T_2\) are related by \(T_1 = \sqrt 3 T_2\). the angles \(\theta _1\) and \(\theta _2\) are

(1) \(\theta _1 = 30 ^\circ \ \theta _2= 60 ^\circ\) with \(T_ 2 = \frac{3mg}{4}\)

(2) \(\theta _1 = 60 ^\circ \ \theta _2 = 30^\circ \) with \(T_2 = \frac{mg}{2}\)

(3) \(\theta _1 = 45^\circ \ \theta _2 = 45^\circ \) with \(T_2 = \frac{3 mg}{4}\)

(4) \(\theta _1 = 30^\circ \ \theta _2 = 60^\circ \) with \(T_2 = \frac{4 mg}{5}\)

Answer 1

Correct option is : (2) \(\theta _1 = 60 ^\circ \ \theta_2 = 30^\circ \ \text{with} \ T_2 = \frac{mg}{2}\) 

\(T_1 \sin \theta_1 + T_2 \sin \theta_2 = mg \ \& \ \ T_1 = \sqrt3\ T_2\)

\(T_2 \left[ \sqrt 3 \ \sin\theta_1 + \sin \theta_2\right] = mg\) 

for \(\theta _1 = 60^\circ \ \ \& \ \ \theta_2 = 30^\circ\)

\(T_2 = \frac{mg}{2}\)