Two particles of masses `m_a` and `m_b` and same charge are projected in a perpendicular magnetic field . They travel along circular paths of radius `r_(a)` and `r_(b)` such that `r_(a) gt r_(b)` . Then which is true ?

Options

A. `m_(a) v_(a) gt m_(b) v_(b)`
B. `m_(a) gt m_(b) and v_(a) gt v_(b)`
C. `m_(a) = m_(b) and v_(a) gt v_(b)`
D. `m_(b) v_(b) gt m_(a) v_(a)`

Answer

A

Explanation

Radius of circular path `r_(a) = (m_(a) v_(a))/(q B)`
and `r_(b) = (m_(b)v_(b))/(qB)`
According to question
`r_(a) gt r_(b)`
`therefore (m_(a) v_(a))/(qB) gt (m_(b) v_(b))/(qB)`
or `m_(a) v_(b) gt m_(b) v_(b)`