Question

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 .

Answer 1

Answer:

$0.0110284391534\ N$

$0.0653784219002\ N$

Explanation:

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

$m_1$ = Mass of sphere = 2000 kg

$m_2$ = Mass of other sphere = 2.1 kg

r = Distance between spheres

Force of gravity is given by

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

The gravitational force is $0.0110284391534\ N$

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

The gravitational force is $0.0653784219002\ N$