The mass of Mars is 1/10 times that of Earth, the diameter of Mars is 1/2 that of Earth Quantitative Analysis A. Derive the equation for gravitational, g, due to a planet. B. Let g be the gravitational field strength on Earth's surface. Derive an expression for the gravitational field on the surface of Mars without plugging in a value for the mass or radius of Mars. Argumentation C. A rock is dropped 2.0 meters above the surface of Mars. Does this rock take a longer or a shorter time to fall than a rock dropped 2.0 m above the surface of Earth? D. On the internet, a student finds the following equation for the time an object will take to fall to the ground from a height h, depending on the mass and radius of the planet the object is on: t = underroot 2hG/MR2. Regardless of whether this equation is correct, does it agree with your qualitative reasoning in Part C? In other words, does this equation for t have the expected dependence as reasoned in Part C? E. Another student deriving an equation for the time it takes for an object to fall from heighth makes a mistake and comes up with: t = underroot R2/2GMh. Without deriving the correct equation, how can you tell that this equation is not plausible in other words, that it does not make physical sense? Briefly explain your reasoning,