Correct Answer - Option 1 : T = (m-m
o)c
2
Concept:
Variation of Mass with Velocity
- According to classical physics, the inertial mass of a body is independent of the velocity of light. It is regarding as a constant. However special theory of relativity leads us to the concept of variation of mass with velocity. It follows from the special theory of relativity 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.
\(m = \frac{{{m_o}}}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}\)
This is the relative formula for variation of mass with velocity where m0 is the rest mass and m is the relativistic mass of the body.
Total energy = Rest energy + Kinetic Energy
Since E = mc2
mc2 = moc2 + KE
K E = (m – mo) c2
This can be written as:
\(KE = \left( { \frac{{{m_o}}}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}- {m_0}} \right){c^2}\)
\(KE =m_0c^2 \left( { \frac{{{1}}}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}- {1}} \right)\)
Explanation:
- Total relativistic energy involves the rest mass m0 and relativistic momentum p = mv.
\(E = \sqrt {\left( {{m_0}{c^2}} \right) + {p^2}{c^2}} \)
- According to mass-energy equivalence, The relativistic formula for kinetic energy is:
mc2 = moc2 + KE
K E = (m – mo) c2
