A) 4 : 1
B) 1 : 1
C) 2 : 1
D) 1 : 2
Correct Answer: C
Solution :
Force on charged particle is electric field \[F=qE\] \[\therefore \] Acceleration\[a=\frac{F}{m}=\frac{qE}{m}\] \[\therefore \] Velocity \[v=u+at\] \[=0+\frac{qE}{m}t\] So, kinetic energy \[K=\frac{1}{2}m{{v}^{2}}\] \[=\frac{1}{2}m{{\left( \frac{qE}{m}t \right)}^{2}}\] Ratio of kinetic energies \[=\frac{\frac{1}{2}{{m}_{1}}{{\left( \frac{qE}{{{m}_{1}}}t \right)}^{2}}}{\frac{1}{2}{{m}_{2}}{{\left( \frac{qE}{{{m}_{2}}}t \right)}^{2}}}\] \[=\frac{{{m}_{2}}}{{{m}_{1}}}=\frac{2m}{m}\] \[=\frac{2}{1}=2:1\]
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