Question

Can someone help meeeeee... show how to solve it plzzzzzzzz

Answer 1

Right answer: 64 units

According to the law of universal gravitation, which is a classical physical law that describes the gravitational interaction between different bodies with mass:

`F=G(m_(1)m_(2))/(r^2)`

Where:

`F` is the module of the force exerted between both bodies

`G` is the universal gravitation constant.

`m_(1)` and
`m_(2)` are the masses of both bodies.

`r` is the distance between both bodies

In this case we have a gravitation force
`F_(1)=16units`, given by the formula written at the beginning. Let’s rename the distance
`r` as
`d`:

`F_(1)=G(m_(1)m_(2))/(d^2)` (1)

And we are asked to find the gravitation force
`F_(2)` with a given distance of
`(d)/(2)`:

`F_(2)=G\frac{m_(1)m_(2)}{({(d)/(2))}^(2)}`

`F_(2)=G\frac{m_(1)m_(2)}{{(d^(2))/(4)}}` (2)

The gravity constant is the same for both equations, and we are assuming both masses are constants, as well. So, let’s isolate
`G m_(1)m_(2)` in both equations:

From (1):

`Gm_(1)m_(2)=F_(1){d}^(2)` (3)

From (2):

`Gm_(1)m_(2)=F_(2)\frac{{d}^(2)}{4}` (4)

If (3)=(4):

`F_(1){d}^(2)=F_(2)\frac{{d}^(2)}{4}` (5)

Now we have to find
`F_(2)`:

`F_(2)=F_(1){d}^(2)\frac{4}{{d}^(2)}`

`F_(2)=4F_(1)` (6)

If
`F_(1)=16 units`:

`F_(2)=(4)(16 units)`

`F_(2)=64 units`>>>>This is the new force of attraction