Answer
(a) particle 2
(b) $\frac{1}{4}$
Work Step by Step
(a) We know that the magnetic force is directly proportional to the charge as well as the speed of the particle. It is also given that the particles experience the same force; thus particle 2 has a greater speed because particle 1 has a greater charge.
(b) We can find the required ratio as
$\frac{v_1}{v_2}=\frac{F/q_1Bsin\theta}{F/q_2Bsin\theta}$
$\frac{v_1}{v_2}=\frac{q_2}{q_1}$
$\implies \frac{v_1}{v_2}=\frac{q_2}{4q_1}$
$\implies \frac{v_1}{v_2}=\frac{1}{4}$
