Question

The charge on a particle Y is double the charge on particle X. These two particles X and Y 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. $\left( \frac { 2 R _ { 1 } } { R _ { 2 } } \right) ^ { 2 }$
• B. $\left( \frac { R _ { 1 } } { 2 R _ { 2 } } \right) ^ { 2 }$
• C. $\frac { R _ { 1 } ^ { 2 } } { 2 R _ { 2 } ^ { 2 } }$
• D. $\frac { 2 R _ { 1 } } { R _ { 2 } }$

Answer 1

Answer: (C)

$\frac { R _ { 1 } ^ { 2 } } { 2 R _ { 2 } ^ { 2 } }$

Answer 2

$r = \frac { 1 } { B } \sqrt { \frac { 2 m V } { q } } \Rightarrow r \propto \sqrt { \frac { m } { q } } \Rightarrow \frac { r _ { x } } { r _ { y } } = \sqrt { \frac { m _ { x } } { q _ { x } } \times \frac { q _ { y } } { m _ { y } } }$

$\Rightarrow \frac { R _ { 1 } } { R _ { 2 } } = \sqrt { \frac { m _ { x } } { m _ { y } } \times \frac { 2 } { 1 } } \Rightarrow \frac { m _ { x } } { m _ { y } } = \frac { R _ { 1 } ^ { 2 } } { 2 R _ { 2 } ^ { 2 } }$