Does a faster particle take longer to complete a circle?

A charged particle moves perpendicular to a uniform magnetic field. Its speed is doubled in a separate run, while its mass, charge and the magnetic field remain unchanged.

What is the ratio of the second orbital period to the first?

Organize the givens & assumptions

Same mass and charge
Same magnetic field
Second speed: 2v

Nonrelativistic speeds, negligible energy loss, no electric field. Compare circular motion in the same uniform field.

A $\tfrac12$
B $1$
C $2$
D $4$

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