Question

A body is initially at rest. It explodes into two objects of mass 1 Kg and 2 Kg moving with a speed of 0.6 times the speed of velocity each. What would be the mass of the original body at rest?

(a) 2 Kg

(b) 2.5 Kg

(c) 3.5 Kg

(d) 3.75 Kg

I got this question in a job interview.

This intriguing question comes from Mass Variation with Velocity in chapter Ultrasonics & Relativity of Engineering Physics I

Answer 1

Correct option is (d) 3.75 Kg

For explanation I would say: E0 = mc^2 = γm1c^2 + γm2c^2

E0 = \(\frac{m1C^2}{\sqrt{1-\frac{v^2}{c^2}}} + \frac{m2C^2}{\sqrt{1-\frac{v^2}{c^2}}}\)

m = E/c^2

Therefore,      m = \(\frac{m1+m2}{\sqrt{1-\frac{v^2}{c^2}}}\)

m = 3/0.8

m = 3.75 Kg.