Question

on a different planet, a dog weighs 150 lbs Assume that this 150 lbs is a weight in our usual physics sense (a force), and that on Earth each dog only weighs 5 lbs.
(a) What is the acceleration due to gravity near to the surface of this heavy planet? Express your answer in m/s^2.
(b) let’s also assume that besides the gravity, it is similar Earth, and it has the same density as Earth (ρ = 5513 kg/m3). What is the radius of the planet itself, not its orbit?

Answer 1

(a) Suppose 'm' is the mass of the dog.

g(p) = Acceleration due to gravity to the surface near the heavy planet

g(e) = Acceleration due to gravity near the surface of the earth = 9.81 m/s^2

So, weight of the dog on the heavy planet, W(p) = m*g(p) = 150 lb -------------------------------------------(i)

weight of the dog on the earth, W(e) = m*g(e) = 5 lb ----------------------------------------------------------(ii)

From (i) and (ii) -

m*g(p) / m*g(e) = 150 / 5 = 30

=> g(p) / g(e) = 30

=> g(p) = 30*g(e) = 30*9.81 m/s^2 = 294.3 m/s^2

(b) The expression for gravitational acceleration is -

g(p) = G*M / R^2 = G*(4/3*pi*R^3*) / R^2 = G*(4/3*pi*R*)

=> R = g(p) / [G*(4/3*pi*)]

Put the values -

R = 294.3 / [6.674 x 10^-11 x 4/3 x 3.141 x 5513] = 1.9099 x 10^8 m

So, radius of the planet = 1.9099 x 10^8 m (Answer)