\"00' m a!) Figure 1: Mechanical system for question {a} Q1 {a} For the mechanical system illustrated in figure 1,. suppose m1 = [L5 kg, Tit-g = 2.1] kg and T113 2 {if} kg. Use Newton's second law and linear algebra to find the accelerations of the objects and the tension in the rope. [? marks] {b} The planet 1ivfenus orbits the Sun with a mean orbital radius of LIIJT a: ll]11 m. The mass of the Sun is 1.99 x if?\" kg. Assume a circular orbit, using Kepler's third law, calculate the orbital period of 1Venus in Earth days. (Let Newton's gravitational constant G = as? 2-: ill11 kg'lms'E] [3 marks] {-2} Start from the Lorentz transformation equations to solve the following problems, i.e., explain your working and justify any formulas used! {i} A rod with proper length Tm moves at a speed of [LE-c relative to a stationary observer {where c is the speed of light in a vacuum]. What is the length of the rod when viewed by the observer? {ii} Consider twins Nancy and Drew who are initially on Earth. On their lith birthday, Nancy travels to a star 15 light years away at a constant speed v = {LESS-r, where c is the speed of light. Nancy then turns and travels back to Earth at the same speed. Meanwhile, Drew remains on the Earth. How old are Nancy and Drew when Nancy returns? [11] marks]