Q169 / 200 · Manipal (MET) 2013 · Physics

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
Correct answer
C
its linear momentum will be more than double
D
its linear momentum remains unchanged

Solution

From Einstein's theorem Relativistic momentum $=\frac{m_0 v}{\sqrt{1-v^2 / c^2}}$ Putting $v=2 v$ we get $p=\frac{m_0(2 v)}{\sqrt{1-(2 v)^2 / c^2}}$ $=2\left(\frac{m_0 v}{\sqrt{1-(2 v)^2 / c^2}}\right)$ So the momentum becomes more than the double.

Hence, the correct answer is option: 'C'.

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