Q110 / 120 · VITEEE 2010 · Physics

Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$, Respectively. The ratio of masses of $\mathrm{X}$ and $\mathrm{Y}$ is

  • A
    $\left(\mathrm{R}_{1} / \mathrm{R}_{2}\right)^{-2}$
  • B
    $\left(\mathrm{R}_{2} / \mathrm{R}_{1}\right)$
  • Correct answer
    C
    $\left(\mathrm{R}_{1} / \mathrm{R}_{2}\right)^{2}$
  • D
    $\left(\mathrm{R}_{1} / \mathrm{R}_{2}\right)$

Solution

As we know, $\frac{1}{2} m v^{2}=q V$ or $v=\sqrt{\frac{2 q V}{m}}$ Centripetal force $\frac{m v^{2}}{R}=q \times B \times v$ $\therefore v=\frac{q B R}{m}$ Hence, $\sqrt{\frac{2 q V}{m}}=\frac{q B R}{m}$ or $R=\left(\frac{2 m V}{q}\right)^{1 / 2} \times \frac{1}{B}$ Here, $V, q$ and $B$ are constants. $\therefore R \propto m$ And, $\frac{m_{1}}{m_{2}}=\left(\frac{R_{1}}{R_{2}}\right)^{2}$

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

Relevant Questions