Two objects attract each other gravitationally. if the distance between their centers decreases by a factor of 2, how does the gravitational force between them change?

a)the gravitational force remains unchanged.
b)the gravitational force decreases by a factor of 2.
c)the gravitational force increases by a factor of 2.
d)the gravitational force decreases by a factor of 4.
e)the gravitational force increases by a factor of 4.

E)The gravitational force increases by a factor of 4.

Explanation:

Isaac Newton presented the law of Universal Gravitation in his book published in 1687, "Philosophiae Naturalis Principia Mathematica". According to this Newton's law, the more mass the objects possess, the greater the force of attraction, and the closer they are to each other, the greater that force will be.

All material particles and all bodies attract each other simply by having mass, in direct proportion to their masses. Gravity has an infinite theoretical scope; but, the force is greater if the objects are close, and while they are moving away that force loses intensity in proportion to the square of the distance that separates the bodies. For example, if one object moves away from another three times the distance, then the force of gravity is reduced to the ninth part or vice versa if the distance between objects decreases with a factor of 2, the gravitational force increases a factor of 4.

Newton's law of universal gravitation is expressed as follows :

Fg = G * M1 * M2 / (r12)^2

Where:

Fg: gravitational force

G: it is the universal gravitation constant and is worth approximately 6,674 * 10 -11

M1 and M2: mass of objects

r12: distance between objects

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min