A) \[2\pi \sqrt{\frac{\ell }{g+\sqrt{\frac{{{q}^{2}}}{{{\ell }^{2}}m}}}}\]
B) \[2\pi \sqrt{\frac{\ell }{g-\sqrt{\frac{{{q}^{2}}}{{{\ell }^{2}}m}}}}\]
C) \[2\pi \sqrt{\frac{\ell }{g}}\]
D) \[2\pi \sqrt{\frac{\ell }{g-\left( \frac{{{q}^{2}}}{\ell } \right)}}\]
Correct Answer: C
Solution :
Charge on each bob = q \[\therefore \] force of repulsion between them \[=\frac{{{q}^{2}}}{4\pi {{\varepsilon }_{0}}{{\ell }^{2}}}.\] As this force is mutual, value of g is not affected. Time period remains the same. \[\therefore \]\[t=2\pi \sqrt{\frac{\ell }{g}}.\] Hence, the correction option is [c].
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