Question

Two asteroids exert a gravitational force, F, on each other. Some time later, the asteroids are now three times as far from each other as before. Which of the following represents the gravitational force at this distance? Select one:
a. F/9
b. F/6
c. F/3
d. F/2

Answer 1

Answer:

a.F/9

Explanation:

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the gravitational Force is described by the next equation

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

Where, G  is   the universal gravitational constant, M1 and M2 are the masses of the objects, and r is the distance between then.

Step 1

time 1

Let

m1= mass of the asteroid 1

m2= mass of the asteroid 2

distance 1=r1

put the values into the equation to find the force

$F_{1}=G*\frac{m_{1}*m_{2} }{r^{2} }\\F_{1}=G*\frac{m_{1}*m_{2} }{r_{1}^{2} }$

Step 2

time 2

r2=3r1

$F_{2} =G*\frac{m_{1}*m_{2} }{(3*r_{1} )^{2} }$

Step 3

compare the forces

$F_{1}=G*\frac{m_{1}*m_{2} }{r^{2} }\\F_{2} =G*\frac{m_{1}*m_{2} }{9(r_{1}^{2}) }\\F_{2}=\frac{F_{1}}{9}$

a.F/9

here it is observed that the force is inversely proportional to the square of the distance, at double distance, it is divided into 4, triple in 9, etc.

Have a great day.