Question

What is the mass ‘m’ of a particle, if its rest mass ‘m₀’ moves with a velocity of \(\frac{c}{\sqrt2}\)
1. m₀
2. 0.707 m₀
3. 0.5 m₀
4. 1.414 m₀

Answer 1

Correct Answer - Option 4 : 1.414 m₀

Concept: 

Variation of Mass with Velocity

• By the conventions of classical physics, the inertial mass of a body is independent of the velocity of light. It is regarding as a constant.
• The theory of relativity provides us the concept of variation of mass with velocity. It states that the mass m of a body moving with relativistic velocity v relative to an observer is larger than its m0 when it is at rest.
• According to Einstein, the mass of the body in motion is different from the mass of the body at rest.

\(m = \frac{{{m_o}}}{{\sqrt{1 - \frac{{{v^2}}}{{{c^2}}}} }}\)

Calculation:

Now, It is given that mass m is moving with velocity v = c / √ 2. 

\(m = \frac{{{m_o}}}{{\sqrt{1 - \frac{{{(c/√2)^2}}}{{{c^2}}}} }}\)

\(\implies m = \frac{{{m_o}}}{{\sqrt{1 - \frac{{{(c/√2)^2}}}{{{c^2}}}} }}\)

\(\implies m = \frac{{{m_o}}}{{\sqrt{1 - \frac{{{(c/√2)^2}}}{{{c^2}}}} }}\)

\(\implies m = \frac{{{m_o}}}{{\sqrt{1 - \frac{1}{2}}}}\)

⇒ m = √2 m₀ = 1.414 m0 

So, the correct option is 1.414 m₀ .