Question

By what fraction does the mass of a boy increase when he starts running at a speed of 12 km h⁻¹?

Answer 1

Given: Speed of the boy, v = 12 km h⁻¹ = 10/3 m/s

Let the rest mass of the boy be m.

Kinetic energy of the boy,

\[E = \frac{1}{2}m v^2\]

\[\Rightarrow E = \frac{1}{2}m \left( \frac{10}{3} \right)^2 = \frac{m \times 50}{9}\]

Increase in energy of the body = Kinetic energy of the boy

This increase in energy is converted into mass. Thus,

Increase in mass \[= ∆ m = \frac{E}{c^2}\]

\[ ∆ m = \frac{m \times 50}{9 \times 9 \times {10}^{16}}\]

Fraction increase in mass \[= \frac{∆ m}{m} = \frac{50}{81 \times {10}^{16}}\]

\[ \Rightarrow \frac{∆ m}{m} = \frac{50}{81} \times {10}^{- 16} = 6 . 17 \times {10}^{- 17}\]