From \"Fundamentals of Physics\" Haliday 7th edition Which statements are true?

Question

From "Fundamentals of Physics" Haliday 7th edition

Which statements are true? (Select all that apply.)
1
The charge is positive.
The charge is negative.
The final speed of the particle is greater than v0.
The final speed of the particle is less than v0.
The final speed of the particle is equal to v0.
For an initial speed 0.5v0, T > T0.
For an initial speed 0.5v0, T < T0.
For an initial speed 0.5v0, T = T0.
For an initial speed 0.5v0, the path is more than a half-circle.
For an initial speed 0.5v0, the path is less than a half-circle.
For an initial speed 0.5v0, the path is also a half-circle.

Explanation / Answer

F_B=qv imes B F_c=rac{mv^2}{r} 3. The attempt at a solution I'm fine until I'm asked to halve the velocity. I combined my two equations and found that when v'=0.5v, r'=0.5r. but I'm not sure how that affects the shape of the trajectory. Will the particle still make a semicircle, only now with a smaller radius? If so, it would make sense that the t'>t. But on the other hand, a smaller velocity should result in a longer time!

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