Physics, 18.11.2020 17:10 jenna6891

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

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Answer from: leo4687

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).

Answer from: Quest

2. they have negligible mass.

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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