Question

Two spheres each have a mass of 2.0 x 10 kg. How far apart must they be to exert a
gravitational force of 50 N between them?
a).016 m b) 231 m c) 53,000 m
d) 110,000 m
e) 6.7 x 10" m

Answer 1

Hi there!

We can use the Gravitational Force equation:

$F_g = \frac{Gm_1m_2}{r^2}$

Fg = Gravitational force (N)

m₁, m₂ = mass of spheres (kg)

r² = distance between the spheres

G = Gravitational Constant

We are given the force of gravity, so we can rearrange the equation to solve for r:

$r^2F_g = Gm_1m_2\\\\r = \sqrt{\frac{Gm_1m_2}{F_g}}$

Plug in the given values:

$r = \sqrt{\frac{(6.67*10^{-11})(2.0*10^9)(2.0*10^9)}{50}} = \boxed{231 m}$

Therefore, the correct answer is B) 231 m.