A small charged ball having mass m and charge q is suspended from a rigid support by means of an inextensible thread of length l. It is made to rotate on a horizontal circular path in a uniform, time independent magnetic field of induction B which is directed upward. The time period of revolution of the ball is `T_0.` If the thread is always stretched, calculate the radius of circular path on which the ball moves.

Explanation

To solve the problem step by step, we will analyze the forces acting on the charged ball and derive the radius of the circular path it follows.

### Step 1: Understand the forces acting on the ball
The ball is subjected to three main forces:
1. The gravitational force acting downward: \( F_g = mg \)
2. The tension in the thread acting along the thread: \( T \)
3. The magnetic force acting perpendicular to the velocity of the ball: \( F_m = qvB \)

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