Question

Read the scenario.

A boulder with a mass of 50 kg is sitting in a backyard.

If the boulder were half the mass, what could be said about the gravitational force on the boulder?

A) It would be reduced to one quarter.
B) It would be doubled.
C) It would not change.
D) It would be cut in half.

Answer 1

Answer: D) It would be cut in half.

Explanation:

According to Newton's law of universal gravitation we have the following:

$F=G\frac{m_{1}m_{2}}{r^2}$  (1)

Where:  

$F$ is the module of the attraction force exerted between both bodies  

$G$ is the universal gravitation constant.  

$m_{1}$ is the mass of the backyard and $m_{2}$ is the mass of the boulder

$r$ is the distance between the backyard and the bouder

Now, if the mass of the boulder were half the mass, equation (1) would be:

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

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

Comparing (1) and (2) we can see the gravitational force is reduced to a half.

Hence, the correct option is D:

D) It would be cut in half.