According to Einstein's theory of relativity, as an object approaches the speed of light, its relativistic mass increases. This phenomenon is known as relativistic mass or "mass dilation." The increase in mass occurs due to the energy associated with the object's motion.
The equation for relativistic mass is given by:
m = m0 / sqrt(1 - (v^2 / c^2))
where: m is the relativistic mass of the object, m0 is the rest mass (mass at rest) of the object, v is the velocity of the object, and c is the speed of light in a vacuum.
As the velocity of the object approaches the speed of light (c), the denominator of the equation approaches zero, causing the relativistic mass (m) to become larger. However, it's important to note that this increase in mass does not mean that the object gains physical matter. It is simply a result of the relativistic effects of motion.
For example, if an object with a rest mass of 1 kilogram (m0 = 1 kg) were to travel at half the speed of light (v = 0.5c), we can calculate its relativistic mass:
m = 1 kg / sqrt(1 - (0.5c)^2 / c^2) m ≈ 1.15 kg
So, at half the speed of light, the object's mass would increase to approximately 1.15 kilograms due to relativistic effects. This increase in mass is a consequence of the energy associated with the object's motion.