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QPages 456-457: Q4: HC Verma: Concepts of Physics - Volume 2 The Special Theory of Relativity Pages 456-457: Q4 Solution: Mass of a particle depends on its speed. Does the attraction of …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often replace the rest mass in Newtonian gravity with the relativistic mass $m=gamma m_0$, assuming $F=G M m/r^2$ still holds. In GR the gravitational mass is the invariant mass (or the full stress–energy tensor), so the force on a test particle in a weak field is independent of its speed. Avoid treating $m$ in $F=G M m/r^2$ as $gamma m_0$.

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

Step-by-Step Verified Solution

**Answer:** Yes, the gravitational attraction of the earth on a particle depends on the particle's speed. **Step-by-Step Explanation:** According to relativity, the inertial mass of a particle increases with speed:
m=m01−v2/c2m = \frac{m_0}{\sqrt{1 - v^2/c^2}}
The gravitational force is proportional to the inertial mass (equivalence principle). Hence, the gravitational attraction increases with speed. However, in most practical situations, v≪cv \ll c, so the effect is negligible .

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