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## Homework Statement

density, ρ of the rock is 4000 kg m−3 and that this density is uniform throughout. You have equipment that enables you to measure the time it takes for a small object to fall from rest through a distance of 2.00 m. Your measurement is 8.0 s.

Obtain an expression for ga in terms of the gravitational constant G, the

radius of the asteroid Ra and the density ρ of the asteroid. Hence determine

Ra.

## Homework Equations

F= Gm/ r2

F=mg

volume of sphere= 4/3 * pi * r^3

density= m/v

## The Attempt at a Solution

substituting volume of sphere= 4/3 * pi * r^3 into density= m/v gives-

density= 3m/ ( 4* pi * r^3 )

4/3 * pi * r^3 * density = m

F= Gm/ r2

F= (G*4/3 * pi * r^3 * density) / r^2

F=G*4/3 * pi * r * density

F=mg

mg= G*4/3 * pi * r * density

4/3 * pi * r^3 * density = m

4/3 * pi * r^3 * density* g = G*4/3 * pi * r * density

g= Gr^-2

or g= G / r^2

(is this correct)?