Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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Mass of a Particle Depends on Its Speed. Does the Attraction of the Earth on the Particle Also Depend on the Particle'S Speed? - Physics

Short Note

Mass of a particle depends on its speed. Does the attraction of the earth on the particle also depend on the particle's speed?

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Mass of a particle depends on the relativistic speed v with which it moves as 

\[m = \frac{m_o}{\sqrt{1 - \frac{v^2}{c^2}}}\]

The gravitational force of attraction of Earth is given by

\[F = \frac{GMm}{r^2}\]

\[ \Rightarrow F = \frac{GM m_o}{r^2 \sqrt{1 - \frac{v^2}{c^2}}}\]


This is the only reason responsible for gravitational lengthening in which a photon travelling at a speed c experiences gravitational force.

Concept: Energy and Momentum
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HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 25 The Special Theory of Relativity
Short Answers | Q 4 | Page 457
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