Question

If two objects of the same mass are attracting each other gravitationally,

what happens to the strength of gravity if you double the distance between them?

Answer 1

The strength of gravity between the will be reduced by a factor of
`(1)/(4)`

Step-by-step explanation:

Newtons law of universal gravitation states that the force of gravitational attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of their distance apart.

mathematically represented as,

F=
`(Gm1m2)/(r^(2) )`

where F is the force of gravitational attraction,

G is the universal gravitational constant

m1 is mass of body 1

m2 is mass of body 2

the two bodies.

From the question the distance r is doubled by 2, which means our new equation will be

F2=
`(Gm1m2)/((2r)^(2) )\\`

F2=
`(Gm1m2)/(4r^(2) )`

F2 =
`(1)/(4)F`

Therefore the strength of gravity will be reduced by one quarter