Consider a hypothetical planet that has uniform density and a radius R′=2R, where R is the radius of the Earth.
a. (i) Write the expressions for the acceleration due to gravity g(r) as a function of the distance r from the planet’s centre for the regions (a) 0≤r≤R′ and (b) r≥R′.
b. (ii) Using the expressions of part (i), draw a qualitative graph of g(r) from the centre (r=0) to r=2R′.
c. (iii) Identify the point on your graph where g attains its maximum value. Explain physically why g increases linearly inside the planet and decreases with 1/r2 outside it.
d. (iv) Mark clearly the portions of the curve that are linear and those that are non-linear.