1: The space-time coordinates of two events as measured by O are * = 6 x...

 

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1: The space-time coordinates of two events as measured by O are *₁ = 6 x 10¹m, y1 = 21 = 0m, t₁ = 2 x 10-4 sec and x2 = 12 x 10¹m, 32 = 22 = 0m, t₂ = 1 x 10-4 sec, then (a) What must be the velocity of O' with respect to O if o' mea- sures the two events to occur simultaneously? (b) What is the spatial separation of two events as measured by O'? Que # 02: An observer, at rest with respect to the ground, observes the following collision. A particle of mass m₁ = 3kg moving with velocity u₁ = 4ms-¹ along the z-axis approaches a second particle of mass m₂ = 1kg moving with velocity u₂ = -3ms along the z-axis. After head on collision the ground finds that m2 has velocity u₂ = 3ms-¹ along the z-axis. (a) Find the velocity u; of my after collision? (b) A second observer, O', who is walking with velocity of 2ms-¹ relative to the ground along the z-axis observes the same collision. What are the system momenta before and after the collision as de- termined by him? Que # 03: Check whether the following equations are invariant or not under Galilian transformations (i) c²t²x² - y² - 2² - (ii) dx² + dy² + dz²-c²dt² [Hint: In solving part (ii), first take drivative and then square.] Que # 04: Do the same as in Que # 03, but now with Lorentz transforma- tions. Que #05: Assume that the earth's velocity through the ether is the same as its orbital velocity, so that v 10-4c. Consider a Michelson-Morley experiment where the arms of interferometer are each 10m long and one arm is in the direction of motion of the earth through ether. Calculate difference in time for the two light waves to travel along each of the arms. 1: The space-time coordinates of two events as measured by O are *₁ = 6 x 10¹m, y1 = 21 = 0m, t₁ = 2 x 10-4 sec and x2 = 12 x 10¹m, 32 = 22 = 0m, t₂ = 1 x 10-4 sec, then (a) What must be the velocity of O' with respect to O if o' mea- sures the two events to occur simultaneously? (b) What is the spatial separation of two events as measured by O'? Que # 02: An observer, at rest with respect to the ground, observes the following collision. A particle of mass m₁ = 3kg moving with velocity u₁ = 4ms-¹ along the z-axis approaches a second particle of mass m₂ = 1kg moving with velocity u₂ = -3ms along the z-axis. After head on collision the ground finds that m2 has velocity u₂ = 3ms-¹ along the z-axis. (a) Find the velocity u; of my after collision? (b) A second observer, O', who is walking with velocity of 2ms-¹ relative to the ground along the z-axis observes the same collision. What are the system momenta before and after the collision as de- termined by him? Que # 03: Check whether the following equations are invariant or not under Galilian transformations (i) c²t²x² - y² - 2² - (ii) dx² + dy² + dz²-c²dt² [Hint: In solving part (ii), first take drivative and then square.] Que # 04: Do the same as in Que # 03, but now with Lorentz transforma- tions. Que #05: Assume that the earth's velocity through the ether is the same as its orbital velocity, so that v 10-4c. Consider a Michelson-Morley experiment where the arms of interferometer are each 10m long and one arm is in the direction of motion of the earth through ether. Calculate difference in time for the two light waves to travel along each of the arms.

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Subtracting two Lorentz trans... View the full answer