Two particles X and Y having equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe a circular paths of radii ‘R1’ and ‘R2’ respectively. The ratio of the mass of X to that of Y is

Question

Two particles X and Y having equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe a circular paths of radii ‘R1’ and ‘R2’ respectively. The ratio of the mass of X to that of Y is (A) (r1/r2) (B) √(r1/r2) (C) [(r2/r1)]2 (D) [(r1/r2)]2

Tardigrade Admin · Accepted Answer

Radius of circular path traced by a particle

r = \frac{m v}{Bq}

Kinetic energy

K = \frac{1}{2} m v^{2} = e V

∴ r = \frac{m ^{2} v ^{2}}{Bq} = \frac{2 m K}{Bq}

Or

r = \frac{2 m e V}{Bq}

\Rightarrow m \propto r^{2}

Thus we get the ratio of masses of

X

to

Y \frac{m _{1}}{m _{2}} = [\frac{r _{1}}{r _{2}}]^{2}

Q. Two particles $X$ and $Y$ having equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe a circular paths of radii ‘ $R_{1}$ ’ and ‘ $R_{2}$ ’ respectively. The ratio of the mass of $X$ to that of $Y$ is

$\frac{r _{1}}{r _{2}}$

$\frac{r _{1}}{r _{2}}$

$[\frac{r _{2}}{r _{1}}]^{2}$

$[\frac{r _{1}}{r _{2}}]^{2}$

Q. Two particles X and Y having equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe a circular paths of radii ‘R1​’ and ‘R2​’ respectively. The ratio of the mass of X to that of Y is

r2​r1​​

r2​r1​​​

[r1​r2​​]2

[r2​r1​​]2

Radius of circular path traced by a particle r=Bqmv​ Kinetic energy K=21​mv2=eV ∴r=Bqm2v2​​=Bq2mK​​ Or r=Bq2meV​​ ⇒m∝r2 Thus we get the ratio of masses of X to Ym2​m1​​=[r2​r1​​]2

Q. Two particles $X$ and $Y$ having equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe a circular paths of radii ‘ $R_{1}$ ’ and ‘ $R_{2}$ ’ respectively. The ratio of the mass of $X$ to that of $Y$ is

$\frac{r _{1}}{r _{2}}$

$\frac{r _{1}}{r _{2}}$

$[\frac{r _{2}}{r _{1}}]^{2}$

$[\frac{r _{1}}{r _{2}}]^{2}$