Question

For Einstein’s relation, E^2 – p^2c^2 = _____________

(a) moc^2

(b) mo^2c^4

(c) moc^4

(d) mo^2c^6

The question was posed to me in an internship interview.

My query is from Einstein’s Special Theory of Relativity topic in division Ultrasonics & Relativity of Engineering Physics I

Answer 1

The correct answer is (b) mo^2c^4

The explanation: We know, E = mc^2 and momentum, p = mv

Now, E^2 – p^2c^2 = m^2c^4 – m^2v^2c^2

Now, we know, m = \(\frac{m_0}{\sqrt{1-\frac{V^2}{c^2}}}\)

 Therefore, E^2 – p^2c^2 = m^2c^4(1-v^2/c^2)

=c^4m^2(1-v^2/c^2)

Using, m^2(1-v2/c^2) = mo^2 we get

E^2 – p^2c^2 = mo^2c^4.