A uniform, solid, 2000.0 kgkg sphere has a radius of 5.00 mm. Find the gravitational force this sphere exerts on a 2.10 kgkg point mass placed at the following distances from the center of the sphere: (a) 5.04 mm , and (b) 2.70 mm .

Respuesta :

Answer:

[tex]0.0110284391534\ N[/tex]

[tex]0.0653784219002\ N[/tex]

Explanation:

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

[tex]m_1[/tex] = Mass of sphere = 2000 kg

[tex]m_2[/tex] = Mass of other sphere = 2.1 kg

r = Distance between spheres

Force of gravity is given by

[tex]F=\dfrac{Gm_1m_2}{r^2}\\\Rightarrow F=\dfrac{6.67\times 10^{-11}\times 2000\times 2.1}{(5.04\times 10^{-3})^2}\\\Rightarrow F=0.0110284391534\ N[/tex]

The gravitational force is [tex]0.0110284391534\ N[/tex]

[tex]F=\dfrac{Gm_1m_2}{r^2}\\\Rightarrow F=\dfrac{6.67\times 10^{-11}\times 2000\times 2.1}{(2.07\times 10^{-3})^2}\\\Rightarrow F=0.0653784219002\ N[/tex]

The gravitational force is [tex]0.0653784219002\ N[/tex]