Question:
For a body moving with relativistic speed if the velocity is doubled, then
For a body moving with relativistic speed if the velocity is doubled, then
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As \(v \to c\), \(\gamma \to \infty\), momentum becomes very large.
Updated On: Apr 23, 2026
- its linear momentum is doubled
- its linear momentum will be less than double
- its linear momentum will be more than double
- its linear momentum remains unchanged
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Relativistic momentum \(p = \frac{m_0 v}{\sqrt{1 - v^2/c^2}}\).
Step 2: Detailed Explanation:
When \(v\) is doubled, denominator \(\sqrt{1 - (2v)^2/c^2}\) becomes smaller than \(\sqrt{1 - v^2/c^2}\).
So \(p\) increases by factor more than 2. At non-relativistic speeds, \(p \propto v\). At relativistic speeds, \(p\) increases faster than \(v\).
Step 3: Final Answer:
Thus, momentum becomes more than double.
Relativistic momentum \(p = \frac{m_0 v}{\sqrt{1 - v^2/c^2}}\).
Step 2: Detailed Explanation:
When \(v\) is doubled, denominator \(\sqrt{1 - (2v)^2/c^2}\) becomes smaller than \(\sqrt{1 - v^2/c^2}\).
So \(p\) increases by factor more than 2. At non-relativistic speeds, \(p \propto v\). At relativistic speeds, \(p\) increases faster than \(v\).
Step 3: Final Answer:
Thus, momentum becomes more than double.
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