Question

What would be the mass of the body at rest, if it explodes into two objects of mass 2 kg each moving with a speed 0.8c relative to the original body?

(a) 4 Kg

(b) 5.4 Kg

(c) 6.2 Kg

(d) 6.7 Kg

This question was addressed to me at a job interview.

The doubt is from Law of Addition of Velocities in chapter Ultrasonics & Relativity of Engineering Physics I

Answer 1

Right choice is (d) 6.7 Kg

The explanation: E0 = mc^2 = γm1c^2 + γm2c^2

E0 = \(\frac{2mC^2}{\sqrt{\frac{1-v^2}{C^2}}}\)

m = E/c^2

m = \(\frac{2 X 2}{\sqrt{1-0.64}}\)

m = 6.67 Kg.