Planet X has free-fall acceleration 8 m/s2 at the surface. Planet Y has twice the mass and twice the radius of planet X. On Planet Y what is the free-fall acceleration?
The variants are: g, M, r
Using the graviational equation.
F = mg = G.(m.M)/r^2
Cancelling the m on both sides, then rearranging to give g, M and r on the same side, we get
gx.rx^2/Mx = G = gy.ry^2/My
or,
gx/gy = (Mx/My)*(ry/rx)^2
where, gx = 8 m/s^2, Mx/My = 1/2, ry/rx = 2/1
Substituting,
gx/gy = (1/2)*(2/1)^2 = (1/2)*4 = 2
gy = gx/2 = 8/2 = 4 m/s^2
On Planet Y, the free-fall acceleration is gy = 4 m/s^2