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

Answer

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

      $F = \dfrac{GMm}{r^2}$   when r>R

When Point is inside the Sphere

      $F = \dfrac{GMm}{R^2}\ \dfrac{r}{R}$  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

       $F = \dfrac{GMm}{r^2}$[/tex]

       $F = \dfrac{6.67\times 10^{-11}\times 1800\times 2.3}{5.05^2}$

               F = 1.082 x 10⁻⁸ N

b) r = 2.65 m

      $F = \dfrac{GMm}{R^2}\ \dfrac{r}{R}$

      $F = \dfrac{6.67\times 10^{-11}\times 1800\times 2.3}{5.05^2}\ \dfrac{2.65}{5.05}$

     $F = 5.68\times 10^{-9}\ N$