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

Choice C)

Step-by-step 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'=(2)/(4)G{\frac {m_(1)m_(2)}{r^(2)}}`

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

Substituting the value of the original force:

`\displaystyle F'=(1)/(2)F`

This means the force is halved

Choice C)