Question

Universal Gravitation Problem?

The gravitational force between two small masses A and B when placed a short distance apart is 3.24x10^-7N. What is the gravitational force between these objects if the masses of both A and B are doubled and the distance is tripled?

Answer 1

`4/9 3.24 cdot 10^(-7)`

Explanation:

The force is such that

#abs(M_B(M_A G)/(r_(AB))^2) = abs(M_A(M_B G)/(r_(AB))^2)=3.24 cdot 10^(-7)#

After the modifications

`abs(2M_B(2M_A G)/(3r_(AB))^2) = 4/9abs(M_B(M_A G)/(r_(AB))^2) = 4/9 3.24 cdot 10^(-7)`

Answer 2

The force will decrease to `1.44 xx 10^(-7)` N

Explanation:

This question is asking you to consider that the force of gravity is directly proportional to each mass, and inversely proportional to the square of the distance between the masses.

Let's do it with a minimum of math:

Doubling the mass of only A or B would cause the force to double (this is what direst proportion means). Doubling both increases the force by 2 x 2 (4 times).

Tripling the distance with cause i) the force to decrease, and ii) the change to be by a factor of `3^2` (or 9 times smaller to be exact).

So, put it together: one factor yields a 4x increase, the other a 9x decrease. Overall, the force will be different by a combined factor equal to `4/9`.

`(3.24 xx 10^(-7)) xx 4/9 = 1.44 xx 10^(-7)` N