# Numerical Problems Based on Special Theory of Relativity

Problem 1. The mean life of a meson is 2 x 10– 6 s. Calculate the mean life of a meson moving with a velocity 0.9c?

Hint :

Problem 2. Calculate the rest energy of electron and proton in eV. Given m = 9.11 x 10-31 kg e. and m P = 1.673 x 1()-21 kg.

Hint:                    E = m c2

Problem 3. At what speed will be mass of a body is 2.25 times its rest mass?

Hint:

Problem 4. The binding energy of hydrogen is 13.6 eV. Find the loss of mass in the formation of one atom of hydrogen.

Hint:                                        E =M C2

Problem 5. The rest mass of an electron is 9.1 x w-·31 kg. What will be its mass if it  was moving with 4/51/z the speed of light?

Problem 6. A rocket is chasing enemy’s space-ship. An observer on the earth observes the speed of rocket to be 2.5 x 108m/sec and that of space-ship 2 x l0 8 m/sec. Calculate (i) the  velocity of enemy’s ship as seen by rocket (ii) the velocity of rocket as seen by enemy.

Problem  7. The  rest mass of an electron is 9.1 x 10-31 kg. What will be its mass if it  was moving with 3/511′ the speed of  light.

Hint: M= 9.1 x 10-31 / √ 1-(0.6)2 =11.38 x 10 -31 kg