Question

Two spherical objects have a combined mass of 190 kg . The gravitational attraction between them is 8.27×10−6 N when their centers are 19.0 cm apart.1.) What is the mass of the heavier object? (kg)
2.) What is the mass of the lighter object? (kg)

Answer 1

Explanation:

It is given that,

Let $m_1\ and\ m_2$ are the masses of two objects such that,

$m_1+m_2=190\ kg$............(1)

Force between them, $F=8.27\times 10^{-6}\ N$

Distance between masses, d = 19 cm = 0.19 m

The gravitational force between two masses is given by :

$F=G\dfrac{m_1m_2}{d^2}$  

$m_1m_2=\dfrac{Fd^2}{G}$

$m_1m_2=\dfrac{8.27\times 10^{-6}\times (0.19)^2}{6.67\times 10^{-11}}$

$m_1m_2=4475.96$.............(2)

On solving equation (1) and (2),

Mass of heavier object, $m_1=162.44\ kg$

Mass of lighter object, $m_2=27.55\ kg$

Hence, this is the required solution.