Question

two charge particles having charge q and 2q are moving perpendicular to uniform magnetic field.if the ratio of their masses is 2:3, the ratio of time periods T1:T2 wil be​

Answer 1

time period of charged particle is given by, T = 2πm/qB

where m is mass of charged particle, q is charge and B is magnetic field.

case 1 : charge $q_1=q$, mass $m_1=2m$ Let m is proportionality constant.

Let us consider B is magnetic field

then, time period of 1st particle is $T_1=\frac{2\pi(2m)}{qB}=\frac{4\pi m}{qB}$.........(1)

case 2 : charge$q_2=2q$, mass $m_2=3m$

then, time period of 2nd particle is $T_2=\frac{2\pi(3m)}{2qB}=\frac{3\pi m}{qB}$...........(2)

from equations (1) and (2),

$\frac{T_1}{T_2}=\frac{\frac{4\pi m}{qB}}{\frac{3\pi m}{qB}}=\frac{4}{3}$