Section A
Q1.
(a) Define the angular velocity ω of a rigid body rotating about some axis. Then derive the relation \overrightarrowv = \overrightarrowω × \overrightarrowr for the velocity of a point in the body with position vector \overrightarrowr relative to an origin on the axis. Draw a diagram explaining all the vectors.
(b) A comet of mass m moves towards the Sun with initial velocity v0. The mass of the sun is M and its radius is R. Find the total cross-section σ for striking the Sun. Take the Sun to be at rest and ignore all other bodies.
(c) Obtain the Lorentz transformations for the components of the momentum-energy four vector.
(d) A body executes Simple Harmonic Motion such that its velocity at the mean position is 2.0 m/s and acceleration at one of the extremities is 1.57 \text m/s^2. Calculate the time period of vibration.
(e) Consider that a continuous laser beam which is assumed to be perfectly monochromatic with a wavelength of 6500 Å is chopped into 2 ns pulses using a shutter. Calculate the number of photons in each pulse, if the power of each pulse is 5 mW.