Question

What happens to the gravitational potential energy between two particles if the distance between them is halved? (a) It does not change(b) It is multiplied by 2(c) It is multiplied by 4(d) It is multiplied by 8What happens to the gravitational force between two particles if the distance between them is doubled? (a) It does not change(b) It decreases by a factor of 2(c) It decreases by a factor of 4(d) It decreases by a factor of 8

Answer 1

Answer:

The gravitational potential energy between two particles, if the distance between them is halved, is multiplied by 4 (option c).

Explanation:

The gravitational force is the force of mutual attraction that two objects with mass experience.

The Law of Universal Gravitation enunciated by Newton says that every material particle attracts any other material particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance that separates them. Mathematically this is expressed as:

$F=G*\frac{m1*m2}{r^{2} }$

where m1 and m2 are the masses of the objects, r the distance between them and G a universal constant that receives  the name of constant of gravitation.

If the distance between two particles is reduced by half, then, where F' is the new value of the gravitational force:

$F'=G*\frac{m1*m2}{(\frac{r}{2} )^{2} }$

$F'=G*\frac{m1*m2}{\frac{(r )^{2} }{2^{2} } }$

$F'=G*\frac{m1*m2}{\frac{(r )^{2} }{4} }$

$F'=4*G*\frac{m1*m2}{r^{2} }$

F'=4*F

The gravitational potential energy between two particles, if the distance between them is halved, is multiplied by 4 (option c).