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Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is $6: 5$ and their respective masses ratio is $9: 4$ . Then, the ratio of their charges will be:
Option: 1
$8:5$

Option: 2
$5:4$

Option: 3
$5:3$

Option: 4
$8:7$

Answers (1)

best_answer

$\mathrm{\frac{r_1}{r_2}=\frac{6}{5} \rightarrow(1) }$

$\mathrm{\frac{m_1}{m_2}=\frac{9}{4} \rightarrow(2) }$

$\mathrm{\frac{q_1}{q_2}=?}$
It is given that,

$\mathrm{K E_1=K E_2 }$

$\mathrm{\frac{P_1^2}{2 m_1}=\frac{P_2^2}{2 m_2} }$

$\mathrm{\frac{P_1}{P_2}=\frac{3}{2} \rightarrow 3}$
We know that,

$\mathrm{r=\frac{m v}{q B}=\frac{p}{q B} }$

$\mathrm{\frac{r_1}{r_2}=\frac{p_1}{p_2} \times \frac{q_2}{q_1}}$

$\mathrm{\frac{q_{1}}{q_{2}}=\frac{p_{1}}{p_{2}}\times \frac{r_{1}}{r_{2}}=\frac{3}{2}\times \frac{5}{6}=\frac{5}{4}}$

Hence (2) is correct option.

Posted by

Rishabh

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