NEET-XII-Physics
47: The Special Theory of Relativity
- #4Mass of a particle depends on its speed. Does the attraction of the earth on the particle also depend on the particle’s speed?Ans : Mass of a particle depends on the relativistic speed v with which it moves as `` m=\frac{{m}_{o}}{\sqrt{1-{\displaystyle \frac{{v}^{2}}{{c}^{2}}}}}``.
The gravitational force of attraction of Earth is given by
`` F=\frac{GMm}{{r}^{2}}``
`` \Rightarrow F=\frac{GM{m}_{o}}{{r}^{2}\sqrt{1-{\displaystyle \frac{{v}^{2}}{{c}^{2}}}}}``
Note: This is the only reason responsible for gravitational lengthening in which a photon travelling at a speed c experiences gravitational force.
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