question_answer

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle \[\theta \] should be:

A)  \[{{0}^{o}}\]                                     

B)  \[{{30}^{o}}\]

C)  \[{{45}^{o}}\]                                   

D)  \[{{60}^{o}}\]

Correct Answer: C

Solution :

                 From force diagram shown in figure, \[T=mg\]                             ...(i) and\[2T\cos \theta =\sqrt{2}mg\]                            ...(ii) Combining Eqs.(i) and (ii), we have \[2m\,\cos \theta =\sqrt{2}\,mg\] or                            \[\cos \theta =\frac{1}{\sqrt{2}}\]                            or                            \[\theta ={{45}^{o}}\]