According to Einstein's theory of relativity, as an object approaches the speed of light, its mass appears to increase from the perspective of an observer at rest relative to the object. This phenomenon is known as relativistic mass or apparent mass.
The formula to calculate the relativistic mass of an object moving at a certain velocity is given by:
m = m₀ / √(1 - v²/c²)
Where: m is the relativistic mass of the object, m₀ is the rest mass of the object (its mass at rest), v is the velocity of the object, and c is the speed of light in a vacuum (approximately 299,792 kilometers per second).
Let's consider an example where the rest mass of the body is 1 kilogram (m₀ = 1 kg), and it is moving at half the speed of light (v = 0.5c).
Using the above formula, we can calculate the relativistic mass:
m = 1 kg / √(1 - (0.5c)²/c²) = 1 kg / √(1 - 0.25) = 1 kg / √0.75 ≈ 1.155 kg
So, according to Einstein's theory of relativity, if a body were to travel at half the speed of light, its relativistic mass would appear to be approximately 1.155 times its rest mass. This relativistic mass increase is a consequence of the relativistic effects of time dilation and length contraction at high velocities.