Question

If you double the mass of both Mass 1 and the distance, how does the gravitational force change? A) The force doubles B) The force triples C) the force quadruples D) the force is half E) the force is 1/4

Answer 1

Answer:

Choice C)

Explanation:

Newton’s Universal Law of Gravitation

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

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

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

If m1 and r are doubled, then the new force F' is:

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

Operating:

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

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

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

Substituting the value of the original force:

$\displaystyle F'=\frac{1}{2}F$

This means the force is halved

Choice C)