A particle of mass `m = 0.1 kg` and having positive charge `q = 75 mu C` is suspended from a point by a thread of length `l = 10 cm`. In the space, a uniform horizontal electric field `E = 10^4 NC^-1` exists. The particle is drawn aside so that the thread becomes vertical and then it is projected horizontally with velocity v such that the particle starts to move along a circle with the same constant speed V. Calculate the radius of the circle and speed `v(g = 10 ms^-2)`.

Explanation

To solve the problem, we need to analyze the forces acting on the charged particle and apply the principles of circular motion. Here is a step-by-step solution:

### Step 1: Identify the Forces
The forces acting on the particle are:
- Weight (mg) acting downward.
- Electric force (F_e = qE) acting horizontally due to the electric field.
- Tension (T) in the thread, which has components in both vertical and horizontal directions.

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