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

Answer 1

The correct option is C

its linear momentum will be more than double

Step 1: Given data

The body moving with relativistic speed

From Einstein's theorem

Relativistic momentum $=\frac{m_{0}v}{\sqrt{1-{\displaystyle \frac{v^2}{c^2}}}}$

$v=$ velocity

$c=$ speed of light in a vacuum

$m_0=$mass

Step 2: To find the body's linear momentum

We know

$mv=\frac{m_{0}v}{\sqrt{1-{\displaystyle \frac{v^2}{c^2}}}}$

$p=\frac{m_{0}v}{\sqrt{1-{\displaystyle \frac{v^2}{c^2}}}}$

Putting $v=2v$

We get,

$$\begin{gathered} p=\frac{m_{0}2v}{\sqrt{1-{\displaystyle \frac{{\left(2v\right)}^2}{c^2}}}} \\ =2\left(\frac{m_{0}v}{\sqrt{1-{\displaystyle \frac{{\left(2v\right)}^2}{c^2}}}}\right) \end{gathered}$$

When the velocity is doubled, the relativistic mass also increases hence the linear momentum will be more than double. If an object is changing its velocity that also changing its speed or changing its direction, then it is said to be accelerating. When the velocity increases the acceleration also increases.

Therefore the correct answer is Option C