Question

A uniform, solid, 1500.0 kg sphere has a radius of 5.00 m. Find the gravitational force this sphere exerts on a 2.40 kg point mass placed at the following distances from the center of the sphere: (a) 5.05 m , and (b) 2.30 m .

Answer 1

a) 9.42 *10^-9 N

b) 4.42 * 10^-9 N

Step-by-step explanation:

Given:

- Mass of uniform solid M = 1500 kg

- Radius of sphere R = 5 m

- Point mass m = 2.40 kg

- Center to Center distances R

- Gravitational constant G = 6.674*10^-11

Gravitational force between two bodies outside sphere is given by:

F_g = G*M*m / r^2 r > R

Gravitational force between center of sphere and a point mass within the body is given by:

In this case the contributing force is p*V(r). p: Density of sphere and section Volume of sphere. Only a fraction of total mass of sphere contributes to F_g. Hence,

F(r) = G*p*V*m / r^2 = G*M*m*r / R^3 r < R

where, V = 4/3 pi*r^3 and p = M / (4/3 pi*R^3)

Find:

a) Gravitational force between bodies @ r = 5.05 m > R.

-The gravitational force is as follows:

F_g = 6.674*10^-11*1500*2.4 / 5.05^2

F_g = 9.42 *10^-9 N

b) Gravitational force between bodies @ r = 2.30 m < R

-The gravitational force is as follows:

F_g = 6.674*10^-11*1500*2.4*2.3 / 5^3

F_g = 4.42 *10^-9 N