1Derive the formula \( g = \frac{GM}{R^2} \) for the acceleration due to gravity on the surface of a planet.
2Why does the acceleration due to gravity not depend on the mass of the falling body?
3Jupiter's mass is about 319 times the Earth's, yet its g is only about 2.6 times the Earth's. Why?
4Taking the Earth's mass as 5.972 × 10²⁴ kg, its radius as 6371 km and G = 6.67 × 10⁻¹¹ N m²/kg², calculate g on the Earth's surface.
5Why is g greater at the Earth's poles than at the equator? In which region do objects fall faster?
6What does it mean to say the average value of g on the Earth is 9.81 m/s²? What does this mean for a body thrown upwards?
7A planet has the same mass as the Earth but half its radius. What is g on this planet? (g on the Earth = 9.81 m/s²)
8When we write \( g \propto \frac{1}{R^2} \), what is being kept constant, and why?