The mass of the first bowling ball is $m_{1} = 6.1 mathrm{~kg}$. The mass of the second bowling ball is $m_{2} = 7.2 mathrm{~kg}$. The gravitational force that pulling each bowling ball toward the other is $F = 3.1 times 10^{-9} mathrm{~N}$.

$textbf{Required: }$

Finding the distance between the two bowling balls.

As Newton’s law of universal gravitation, The force of gravity between two objects is given by

$$
begin{align*}
F &= G ~ dfrac{ m_{1} ~ m_{2} }{ r^{2} }
end{align*}
$$

Rearrange and solve for the distance between the two bowling balls:

$$
begin{align*}
r &= sqrt{ G ~ dfrac{ m_{1} ~ m_{2} }{ F} } \
&= sqrt{ 6.67 times 10^{-11} mathrm{~N cdot m^{2}/kg^{2}} ~ dfrac{ 6.1 mathrm{~kg} times 7.2 mathrm{~kg} }{ 3.1 times 10^{-9} mathrm{~N} } } \
&= 0.972 mathrm{~m}
end{align*}
$$

So, the distance between the two bowling balls is $0.972 mathrm{~m}$.

The distance between the two cars is $r = 4.7 mathrm{~m}$. The gravitational force between the two cars is $F = 4.5 times 10^{-6} mathrm{~N}$.

$textbf{Required: }$

Finding the mass of each car.

Solve for the two cars are identical $m_{1} = m_{2}$:

As Newton’s law of universal gravitation, The force of gravity between two objects is given by

$$
begin{align*}
F &= G ~ dfrac{ m_{1} ~ m_{2} }{ r^{2} } \
&=G ~ dfrac{ m^{2} }{ r^{2} } \
end{align*}
$$

Rearrange and solve for the mass of each car:

$$
begin{align*}
m &= sqrt{ dfrac{ F ~ r^{2} }{ G} } \
&= sqrt{ dfrac{ 4.5 times 10^{-6} mathrm{~N} times left( 4.7 mathrm{~m} right)^{2} }{6.67 times 10^{-11} mathrm{~N cdot m^{2}/kg^{2}} }} \
&= 1220.791 mathrm{~kg}
end{align*}
$$

So, the mass of each car is $1220.791 mathrm{~kg}$.