Question

Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of both objects was tripled, and if the distance between the objects was doubled, then what would be the new force of attraction between the two objects?

Answer 1

Answer:

The new force of attraction would be 36 units

Explanation:

Law of Universal Gravitation

Objects attract each other with a force that is proportional to their masses and inversely proportional to the square of the distance.  

This statement can be expressed with the formula:

$\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}$

Where:

m1 = mass of object 1

m2 = mass of object 2

r     = distance between the objects' center of masses

G   = gravitational constant: $6.67\cdot 10^{-11}~Nw*m^2/Kg^2$

Now suppose two given objects attract with a force of F=16 units, thus:

$\displaystyle G{\frac {m_{1}m_{2}}{r^{2}}}=16$

And now the masses of both objects is tripled, i.e., m1'=3m1, m2'=3m2, and the distance between them is doubled, r'=2r. The new force is:

$\displaystyle F'=G{\frac {3m_{1}3m_{2}}{(2r)^{2}}}$

Operating:

$\displaystyle F'=G{\frac {9m_{1}m_{2}}{4r^{2}}}$

$\displaystyle F'=\frac{9}{4}G{\frac {m_{1}m_{2}}{r^{2}}}$

Substituting the value of the initial force:

$\displaystyle F'=\frac{9}{4}\cdot 16$

$F'=36\ units$

The new force of attraction would be 36 units