High School

If the force of gravity between two identical masses is [tex]5.00 \times 10^{-8} \, \text{N}[/tex] and they are [tex]5.00 \, \text{m}[/tex] apart, what is the mass of each object?

Answer :

The mass of each object is 13.7 kg.

Given:

Force of gravity (F) = 5.00 x 10^-8 N

Distance between the masses (r) = 5.00 m

Gravitational constant (G) = 6.67 x 10^-11 N m^2/kg^2

The force of gravity between two masses is given by the formula:

F = G * (m1 * m2) / r^2

Since the masses are identical, m1 = m2 = m:

F = G * m^2 / r^2

Substitute the given values into the formula:

5.00 x 10^-8 = 6.67 x 10^-11 * m^2 / 5.00^2

Solve for the mass (m):

m^2 = (5.00 x 10^-8 * 5.00^2) / 6.67 x 10^-11

m^2 = 1.25 x 10^-6 / 6.67 x 10^-11

m^2 = 187.5

m = √187.5

m ≈ 13.7 kg

Since the masses are identical, each object has a mass of 13.7 kg.