question_answer

Two small spheres of masses \[{{M}_{1}}\] and \[{{M}_{2}}\]are suspended by weightless insulating threads of lengths \[{{L}_{1}}\] and \[{{L}_{2}}\]. The spheres carry charges \[{{Q}_{1}}\] and \[{{Q}_{2}}\] respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of \[{{\theta }_{1}}\] and \[{{\theta }_{2}}\] as shown. Which one of the following conditions is essential, if \[{{\theta }_{1}}={{\theta }_{2}}\]?

A) \[{{M}_{1}}\ne {{M}_{2}},\] but \[{{Q}_{1}}={{Q}_{2}}\]

B) \[{{M}_{1}}={{M}_{2}}\]

C) \[{{Q}_{1}}={{Q}_{2}}\]                

D) \[{{L}_{1}}={{L}_{2}}\]

Correct Answer: B

Solution :

For sphere 1, in equilibrium