Magnetic Effects Of Current Question 296
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 [MP PET 1997]
Options:
A) $ {{( \frac{2R_{1}}{R_{2}} )}^{2}} $
B) $ {{( \frac{R_{1}}{2R_{2}} )}^{2}} $
C) $ \frac{R_{1}^{2}}{2R_{2}^{2}} $
D) $ \frac{2R_{1}}{R_{2}} $
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Answer:
Correct Answer: C
Solution:
$ r=\frac{1}{B}\sqrt{\frac{2mV}{q}}\Rightarrow r\propto \sqrt{\frac{m}{q}}\Rightarrow \frac{r_{x}}{r_{y}}\times \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}}{2R_{2}^{2}} $
BETA
