When a boy starts running at a speed of 12 km h ⁻¹ , by what fraction does his mass increase?

Step-by-step solution

Speed v = 12 km h ⁻¹ = 12 5 18 m s ⁻¹ = 10 3 m s ⁻¹ The relativistic mass is given by m = m₀ 1 - v^2 c^2 The fractional increase in mass is m m₀ = m - m₀ m₀ = (1 - v^2 c^2 )^ -1/2 - 1 Since v c , using the binomial expansion: m m₀ (1 + 1 2 v^2 c^2 ) - 1 = 1 2 v^2 c^2 Substituting the values: m m₀ = 1 2 ( 10 3 )^2 (3 10^8)^2 m m₀ = 1 2 100 9 9 10¹⁶ = 100 162 10¹⁶ m m₀ = 1 1.62 10⁻¹⁶ 6.17 10⁻¹⁷