A grounded metallic sphere oscillating!

Classical Mechanics Level 5

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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