Q146 / 160 · AP EAMCET 2003 · Physics

Two ions having masses in the ratio $1: 1$ and charges $1: 2$ are projected into uniform magnetic field perpendicular to the field with speeds in the ratio $2: 3$. The ratio of the radii of circular paths along which the two particles move is :

  • Correct answer
    A
    $4: 3$
  • B
    $2: 3$
  • C
    $3: 1$
  • D
    $1: 4$

Solution

$m_1: m_2=1: 1$ $q_1: q_2=1: 2$ $v_1: v_2=2: 3$ Radius of path of chaged particle moving in uniform magnetic field, $r=\frac{m v}{B q}$ $\therefore \quad \frac{r_1}{r_2}=\left(\frac{m_1}{m_2}\right)\left(\frac{v_1}{v_2}\right) \times\left(\frac{q_2}{q_1}\right)$ $=\frac{1}{1} \times \frac{2}{3} \times \frac{2}{1}=\frac{4}{3}$ $r_1: r_2=4: 3$

Hence, the correct answer is option: 'A'.

Relevant Questions