Question

Two particles X and Y having equal charge, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The ratio of the mass of X to that of Y is

• A. $\sqrt{\frac{R_1}{R_2}}$
• B. $(\frac{R_2}{R_1}{)}^2$
• C. $(\frac{R_1}{R_2}{)}^2$
• D. $\sqrt{\frac{R_2}{R_1}}$

Answer 1

Answer: (C)

$(\frac{R_1}{R_2}{)}^2$

$m_1{v}_1^2=m_2{v}_2^2$

work done on each particle =qV

where V is potential difference and q is charge.

assuming particle starts from rest.The final kinetic energy will be

${\frac{1}{2}m}_1{v}_1^2=qv$

${\frac{1}{2}m}_2{v}_2^2=qv$

${m_1{v}_1^2=m}_2{v}_2^2$

let magnetic feild be B then

magnetic force on each particle will be
$F_{m1}=q{V}_{1}B$

$F_{m2}=q{V}_{2}B$

$\frac{m_1{v}_1^2}{R_1}=qB{v}_1=m_1{v}_1=qB{R}_1$

$\frac{m_2{v}_2^2}{R_2}=qB{v}_2=m_2{v}_2=qB{R}_2$

$m_1{\left(\frac{qB{R}_1}{m_1}\right)}^2=m_2{\left(\frac{qB{R}_2}{m_2}\right)}^2$

$\frac{R_1^2}{m_1}=\frac{R_2^2}{m_2}$

$\frac{m_1}{m_2}={\left(\frac{R_1}{R_2}\right)}^2$