CSS 2020 Physics Paper I

(a) What is the curl of a vector field? Explain its physical significance. (b) What is vector triple product? Show that A x (B x C) = (A.C)B - (A.B)C. (c) If Φ = 2x³y²z⁴ then find the div(grad Φ).

(a) State and explain Kepler's law of areas. (b) A spaceship of mass m = 4.50 x 10³ kg is in a circular Earth orbit of radius r = 8.00 x 10⁶ m and period T₀ = 7.119 x 10³ s. A thruster is fired to decrease the speed to 96% of the original. What is the period of the resulting elliptical orbit?

Which has greater magnitude: the angular momentum of the Earth (relative to its center) associated with its rotation on its axis or the angular momentum of the Earth (relative to the center of its orbit) associated with its orbital motion?

(a) Explain the equivalence of mass and energy. (b) Explain two tests of time dilation, specifically focusing on microscopic and macroscopic clocks.