A) \[T=2\pi r\sqrt{\frac{m}{2k\lambda q}}\]
B) \[{{T}^{2}}=\frac{4{{\pi }^{2}}m}{2k\lambda q}{{r}^{3}}\]
C) \[T=\frac{1}{2\pi r}\sqrt{\frac{2k\lambda q}{m}}\]
D) \[T=\frac{1}{2\pi r}\sqrt{\frac{m}{2k\lambda q}}\]
Correct Answer: A
Solution :
[a] We have centripetal force equation \[q\left( \frac{2k\lambda }{r} \right)=\frac{m{{v}^{2}}}{r}\text{ so }v=\sqrt{\frac{2kq\lambda }{m}}\] \[\text{Now, }T=\frac{2\pi r}{v}=2\pi r\sqrt{\frac{m}{2kq\lambda }}\text{ where }k=\frac{1}{4\pi {{\varepsilon }_{0}}}\]
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