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Therefore, for a particle’s relativistic mass to be 20% higher than rest mass, its velocity must be . In the equation of relativistic mass, if the velocity of an object becomes equal to the speed of light, then its mass becomes infinite.
Calculating it out further it gives a speed of 2.598 •10^8 m/s. This tells you that for any mass, whether a proton, or a neutrino, or a 1,000,000 Kg giant spaceship, for its mass to be doubled the mass would have to reach 0.866c in speed or a speed of 2.598 • 10^8 m/s…
So I think the equivalent question is “at what speed does an electron’s energy become twice its mass?” as γ=1/1−v2/c2−−−−−−−−√=E/mc2. Take the square root again and you get the relevant speed as a fraction of c.
When the mass of an electron becomes equal to thrice its rest mass, its speed is.
The rest mass is the mass of a particle (in our case the photon) as measured by an observer who sees the particle still and with zero speed. Thus comes the term REST mass. But according to special relativity, light ALWAYS travels with the light speed c, and is NEVER at rest. And so it has zero REST mass.
constant speed otherwise Einsteins General Relativity will work here. According to your question , => Lorentz factor is 4.
Near the speed of light, the mass is so high that it reaches infinity, and would require infinite energy to move it, thus capping how fast an object can move. The only reason light moves at the speed it does is because photons, the quantum particles that make up light, have a mass of zero.
If ‘mass’ is defined as “how much momentum you have to spend to increase v by one unit”, then the ‘mass’ does increase — it would take an infinite amount of momentum to reach the speed of light.
The correct option is (C) {(√3c) / 2}.
As per the question m’ = 2m. We are asked to calculate the speed of the particle. As per Einstein’s theory of relativity, Here v is the velocity of the body and c is the velocity of light.
So a proton observed at % the speed of light will have an equal amount of rest energy to kinetic energy. That is about m/s. so v=0.866 c is the velocity of the particle which double its rest mass.
For starters, whereas the rest mass of an object is an intrinsic property, kinetic energy is not: it depends on the observer. Either way, doubling the “relativistic mass” means doubling the total energy, as the proportionality factor between the two, the vacuum speed of light squared, remains the same.
When the kinetic energy is equal to mc2, the object’s velocity will be about 87% of the speed of light.
Kinetic energy is directly proportional to the mass of the object and to the square of its velocity: K.E. = 1/2 m v2. If the mass has units of kilograms and the velocity of meters per second, the kinetic energy has units of kilograms-meters squared per second squared.