# A grounded metallic sphere oscillating!

In the figure, a solid metallic grounded sphere of mass $$m$$ and radius $$R$$is suspended from a ceiling as shown. The length of string is $$L$$ and the distance between ceiling and floor is $$2L$$. At the floor, directly below the point of suspension is a fixed point charge $$q$$.

Find the time period of small oscillations in the vertical plane of the sphere in seconds

Details and assumptions:

1) The sphere is grounded by means of a long slack wire that doesn't interrupt its motion

2) $$m = 1 Kg$$

3) $$g = 9.8 m/s^2$$

4) $$L = 50 \text{cm}$$

5) $$R = 25 \text{cm}$$

6) $$q = 10 \mu C$$

7) $$k = \frac{1}{4 \pi \epsilon_{0}} = 9 \times 10^9 N m^2/C^2$$

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