Question

A uniform, solid, 1800.0 kgkg sphere has a radius of 5.00 mm. Find the gravitational force this sphere exerts on a 2.30 kgkg point mass placed at the following distances from the center of the sphere: (a) 5.05 mm , and (b) 2.65 mm .

Answer 1

given,

Mass of the solid sphere = 1800 Kg

radius of the sphere,R = 5 m

mass of the small sphere, m = 2.30 Kg

when the Point is outside the sphere the Force between them is equal to

`F = (GMm)/(r^2)` when r>R

When Point is inside the Sphere

`F = (GMm)/(R^2)\ (r)/(R)` when r<R

where r is the distance where the point mass is placed form the center

Now Force calculation

a) r = 5.05 m

`F = (GMm)/(r^2)`[/tex]

`F = (6.67* 10^(-11)* 1800* 2.3)/(5.05^2)`

F = 1.082 x 10⁻⁸ N

b) r = 2.65 m

`F = (GMm)/(R^2)\ (r)/(R)`

`F = (6.67* 10^(-11)* 1800* 2.3)/(5.05^2)\ (2.65)/(5.05)`

`F = 5.68* 10^(-9)\ N`