# Relativistic Mass Formula

Relativistic mass refers to mass of a body which change with the speed of the body as this speeds approaches close to speed of light, it increases with velocity and tends to infinity when the velocity approaches the speed of light.

Relativistic mass = rest mass / squared root [one minus (velocity / speed of light) squared]

The equation is:

m_{r} = m_{0} / sqrt (1 – v^{2} / c^{2} )

Where:

m_{r}: relativistic mass

m_{0}: rest mass (invariant mass)

v: velocity

c: speed of light

Relativistic Mass Formula Questions:

1) An electron has a rest mass of 9.11 x 10 ^{-31} kg. In a detector, the same electron has a mass of 12.55 x 10^{-31} kg. How fast is electron moving relative the detector?

Answer:

We cleared the velocity of the equation of the relativistic mass

v = c √(1 – (m_{0} / m_{r})^{2}

Now we replace the data

v = (3.00 x 10^{8} m/s) √(1 – 9.11 x 10^{-31} kg / 12.55 x 10^{-31} kg)

v = 2.06 x 10^{8} m/s

2) The rest mass of an electron is 9.1 x 10^{-31} kg and it moves with a speed of 4.5 x 10^{5} m/s. Calculate the relativistic mass.

Answer:

We juts replace the data in the relativistic mass equation

m_{r} = 9.1 x 10 ^{-31} kg / sqrt (1 – (4.5 x 10^{7} m/s / 3.0 x 10^{8} m/s)^{2})

m_{r} = 9.8 x 10^{-31} kg

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