Q.3 The visible disk of our Milky Way galaxy is about 105 light-years in diameter. A cosmic-ray proton enters the galactic plane with speed v = 0.99c. How long would it take the proton to cross teh galaxy from our point of view? What would be the corresponding time if measured from proton's frame? How wide is the galactic plane to the proton, in its direction of motion? Q.4 In order to prolong one's life, observer A starts a journey leaving observer B behind. If A moves a round trip at the steady rate of 5 x 102m/s for 102s according to the clock of B, how much less have A aged than B? Q.5 For some arbitrary function f check the Lorentz invariance of (i) Schroedinger's equation, (ii) Wave equation, (iii) Klein-Gordon equation.