Physics

If you are given the density and radius of planet X, how would you calculate
the acceleration of gravity on the surface of this planet?

As we know

F=ma (here a=g)

F=GMm/r^2 (newtons law of gravitation)

Therefore equating both forces we get

g=GM/r^2 --------------(1)

As we know density(þ)=Mass(M)/volume

But earth is sphere therefore volume of earth is 4/3(pie)×r^3

Therefore mass(M)=þ×4/3(pie)r^3

Substituting value of Mass M in equation 1

Therefore

g=Gþ4/3(pie)r