# Relativistic Mass Formula

Relativistic Mass Formula

The mass concept dialogue is a very standard one in physics. The well known special theory of relativity voices a lot more about relativistic mass, when there is comparative measurements of length and time in dissimilar frames. The relative change in mass is also perceived when the body is in motion. This concept is relativistic mass. Comparable to length contraction and time dilation a thing called mass increase happens when the object is in motion.

The relativistic mass formula is articulated as,

$m=\frac{m_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$

Where,
the rest mass is mo ,

the velocity of the moving body is,

Velocity of light is

Relativistic Mass Solved Examples

Some solved problems are given below based on Relativistic Mass:

Problem 1: An object in motion has mass of a 12 kg and travels in the air with velocity 0.82. What would be its rest mass?

Known:

(Mass) m = 12 kg,

(Velocity) v = 0.82c,

c = 3 × 1088 m/s22.

The relativistic mass formula is articulated as,

$m=\frac{m_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$

$12=\frac{m_{0}}{\sqrt{1-\frac{(0.82)^{2}c^{2}}{c^{2}}}}$

Rest mass, mo = 7.2 kg (approximately)

Thus, the rest mass of the given object is 7.2 kg.

Problem 2: A particle of mass 1.67 × 10−24 kg travels with velocity 0.65. Compute its rest mass?

Given: Mass m = 1.67 × 10−24kg, v = 0.65c, c = 3 × 108 m/s2.

The relativistic mass formula is articulated as,

$m=\frac{m_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$

$1.67\times10^{-24}=\frac{m_{0}}{\sqrt{1-\frac{(0.65)^{2}c^{2}}{c^{2}}}}$

Rest mass, mo = 1.26 × 10−24 kg (approximately).

Thus, the rest mass of the particle is 1.26 × 10−24 kg.

#### Practise This Question

Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1,T2), volume (V1,V2) and pressure (P1,P2) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be