NEET-XII-Physics
47: The Special Theory of Relativity
- #4Which of the following quantities related to an electron has a finite upper limit?
(a) Mass
(b) Momentum
(c) Speed
(d) Kinetic energydigAnsr: cAns : (c) speed
If an electron is given a very high speed v, its mass
`` m=\gamma {m}_{o}=\frac{{m}_{o}}{\sqrt{1-{\displaystyle \frac{{v}^{2}}{{c}^{2}}}}}``
`` \,\mathrm{\,momentum\,},p=mv=\gamma {m}_{o}v=\frac{{m}_{o}v}{\sqrt{1-{\displaystyle \frac{{v}^{2}}{{c}^{2}}}}}``
`` \,\mathrm{\,kinetic\,}\,\mathrm{\,energy\,},k=\frac{1}{2}m{v}^{2}=\frac{1}{2}\gamma {m}_{o}{v}^{2}=\frac{1}{2}\frac{{m}_{o}{v}^{2}}{\sqrt{1-{\displaystyle \frac{{v}^{2}}{{c}^{2}}}}}``
`` \gamma =\frac{1}{\sqrt{1-{\displaystyle \frac{{v}^{2}}{{c}^{2}}}}}``
`` \,\mathrm{\,at\,}v=c,\gamma =\frac{1}{\sqrt{1-{\displaystyle \frac{{c}^{2}}{{c}^{2}}}}}=\infty ``
`` \Rightarrow \,\mathrm{\,at\,}v=c,m=p=k=\infty ``
Therefore, there's an upper bound for v to be always less than c but no upper limits for mass, momentum and kinetic energy of the electron.
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