Two particles A and B have equal charges but different masses $\mathrm{M}_{\mathrm{A}}$ and…

Two particles A and B have equal charges but different masses $\mathrm{M}_{\mathrm{A}}$ and $\mathrm{M}_{\mathrm{B}}$. After being accelerated through same potential difference enter the region of uniform magnetic field and describe the path of radii $\mathrm{R}_{\mathrm{A}}$ and $\mathrm{R}_{\mathrm{B}}$ respectively. Then $\mathrm{M}_{\mathrm{A}}: \mathrm{M}_{\mathrm{B}}$ is
  1. $\frac{\mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{B}}}$
  2. $\frac{\mathrm{R}_{\mathrm{B}}}{\mathrm{R}_{\mathrm{A}}}$
  3. $\left(\frac{\mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{B}}}\right)^{2}$
  4. $\left(\frac{\mathrm{R}_{\mathrm{B}}}{\mathrm{R}_{\mathrm{A}}}\right)^{2}$

Solution

Two particles $A$ and $B$ have equal charges but different masses $M_A$ and $M_B$. After being accelerated through the same potential difference, they enter a region of uniform magnetic field and describe paths with radii $R_A$ and $R_B$. The ratio $M_A: M_B$ is related to $R_A: R_B$ as: $\left(\frac{R_A}{R_B}\right)^2: 1$

Asked in: MHT CET 2020 (12 Oct Shift 2)

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