Two particles `A` and `B` of masses `m_A` and `m_B` respectively and having the same charge are moving ina plane. A uniform magnetic field exists perependicular to this plane. The speeds of the particles are `v_A` and `v_B` respectively and the trajectories are as shown in the figure. Then,

Options

A. `m_Av_Altm_Bv_B`
B. `m_Av_Agtm_Bv_B`
C. `m_Altm_B and v_Altv_B`
D. `m_A=m_B and v_A=v_B`

Answer

b

Explanation

When a charged particle is moving at right angle to the
magnetic field, then a force acts on it which behaves as a
centripetal force and moves the particle in circular path.

`:. (m_Av_A^2)/(2r)=qv_AB :. (m_Av_A)/(2r)=qB`
Similarly, for second particle moving with half radius as
compared to the first one, we have
`(m_Bv_B)/r=qBimplies (m_Av_A)/(2r)=(m_Bv_B)/r implies (m_Av_A)=2(m_Bv_B)`
`implies m_Av_Agtm_Bv_B`
`:.` Correct option (b).