Answer to Question #295328 in Mechanics | Relativity for Paul

Question

The rest mass of an electron is 9.1 x

10^-31 kg. What is the relativistic mass if its velocity is 55 % of the speed

of light?

Answer 1

Explanation & Calculation

• The relativistic mass is given by the following formula and upon substitution of the given values into it, you can get the answer.

$\qquad\qquad \begin{aligned} \small M_{relativistic}&=\small \frac{m_{rest}}{\sqrt{1-\large\frac{v^2}{c^2}}} \end{aligned}$

• Here the speed is

$\qquad\qquad \begin{aligned} \small v&=\small \frac{55}{100}c\\ \implies \small \frac{v^2}{c^2}&=\small\frac{55^2}{100^2} \end{aligned}$

• Then the required answer is

$\qquad\qquad \begin{aligned} \small M_r&=\small \frac{9.1\times10^{-31}\,kg}{\sqrt{1-\frac{55^2}{100^2}}}\\ &=\small 1.1\times10^{-30}\,kg\cdots(\text{increased}) \end{aligned}$