Question

Two planets have the same surface gravity, but planet b has twice the radius of planet

a. if planet a has mass m, what is the mass of planet b?
a.m/
b.m
c.m
d.4m
e.m/4

Answer 1

The formula for the acceleration due to gravity is:

a = Gm/r²
where
G is the universal gravitational constant = 6.6726 x 10⁻¹¹ N-m²/kg²
m is the mass of planet
r is the radius of planet

So, if they have the same a:

m₁/r₁² = m₂/r₂²
So, if m₁ = m and r₂ = 2r₁,
m/r₁² = m₂/(2r₁)²
m₂ = 4m

Thus, the answer is D.