Question

For a body moving with relativistic speed if the velocity is doubled, then

• A. its linear momentum is doubled
• B. its linear momentum will be less than double
• C. its linear momentum will be more than double
• D. its linear momentum remains unchanged

Hint:

As \(v \to c\), \(\gamma \to \infty\), momentum becomes very large.

Answer 1

The Correct Option is C

Step 1: Concept:
Relativistic momentum \(p = \frac{m_0 v}{\sqrt{1 - v^2/c^2}}\).
Step 2: 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: Conclusion:
Thus, momentum becomes more than double.