1. Magnetic force provides the centripetal force

For a charged particle moving perpendicular to a magnetic field, the magnetic force is

$F = qvB$

This acts as the centripetal force needed for circular motion:

$qvB = \frac{mv^2}{r}$

2. Solve for the speed $v$

Cancelling one factor of $v$:

$qB = \frac{mv}{r}$

So,

$v = \frac{qBr}{m}$

3. Use time period formula

The time taken for one complete revolution is

$T = \frac{\text{circumference}}{\text{speed}} = \frac{2\pi r}{v}$

Substitute $v = \dfrac{qBr}{m}$:

$T = \frac{2\pi r}{qBr/m}$

$T = 2\pi r \cdot \frac{m}{qBr}$

$T = \frac{2\pi m}{qB}$

4. Match with the options

$T = \frac{2\pi m}{qB}$

This corresponds to Option C.

5. Comparison with stored answer

Stored correct answer: C
Derived answer: C
So, the derived answer agrees with the stored correct answer.