question_answer

Two small spherical balls each carrying a charge \[Q=10\mu C\] (10 micro-coulomb) are suspended by two insulating threads of equal lengths 1m each, from a point fixed in the ceiling. It is found that in equilibrium threads are separated by an angle \[{{60}^{o}}\] between them, as shown in the figure. What is the tension in the threads (Given: \[\frac{1}{(4\pi {{\varepsilon }_{0}})}=9\times {{10}^{9}}Nm/{{C}^{2}}\])               [MP PET 2001; Pb PET 2003]

A)            18 N

B)            1.8 N

C)            0.18 N

D)            None of the above

Correct Answer: B

Solution :

             In the following figure, in equilibrium\[{{F}_{e}}=Tsin\text{ }{{30}^{o}}\],     r = 1m Þ \[9\times {{10}^{9}}.\frac{{{Q}^{2}}}{{{r}^{2}}}\]=\[T\times \frac{1}{2}\] Þ \[9\times {{10}^{9}}.\frac{{{(10\times {{10}^{-6}})}^{2}}}{{{1}^{2}}}=T\times \frac{1}{2}\] \[\Rightarrow \]T = 1.8 N