question_answer

A 60 kg block is suspended by two cables as shown in the figure. The ratio of tensions \[{{T}_{1}}\] and \[{{T}_{2}}\]is

A) \[\sqrt{3}:1\]               

B) \[1:\sqrt{3}\]   

C)      \[2:\sqrt{3}\]   

D)      \[\sqrt{3}:2\]    

Correct Answer: A

Solution :

For the equilibrium of the point O, the horizontal components of the tensions must be equal. \[{{T}_{1}}\sin {{30}^{o}}={{T}_{2}}\sin {{60}^{o}}\] or, \[{{T}_{1}}\times \frac{1}{2}={{T}_{2}}\frac{\sqrt{3}}{2}\] or, \[\frac{{{T}_{1}}}{{{T}_{2}}}=\sqrt{3}\]  Hence, the correction option is (a).