A) The time of fall will be more in case of electron
B) The time of fall will be more in case of proton
C) The time of fall will be same in both cases
D) The time of fall will be independent of charge
Correct Answer: B
Solution :
The magnitude of electric field is given by \[E=\frac{F}{{{q}_{0}}}\] or \[F={{q}_{0}}E\] or \[ma={{q}_{0}}E\] \[a=\frac{{{q}_{0}}E}{m}\] Now, distance covered by charge in electric field is given by \[s=\frac{1}{2}a{{t}^{2}}\] or \[s=\frac{1}{2}\left( \frac{{{q}_{0}}E}{m} \right){{t}^{2}}\] ?(ii) [using Eq. (i)] Hence, time required to cover the distance s comes out to be \[t=\sqrt{\frac{2sm}{{{q}_{0}}E}}\] \[\Rightarrow \] \[{{t}^{2}}\propto m\] Since, \[{{m}_{p}}>{{m}_{e}}\] hence, a proton takes more time to cover the same distance in the uniform electric field of same magnitude.
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