00:01
We are given four graphs here of gravitational force versus separation between two masses.
00:10
We are to determine which of the following graphs correctly shows gravitational force as a function of separation.
00:17
So we will use the definition of gravitational force that's written here in red ink.
00:23
And, oops, know that the denominator, i mean the numerator here is, constant so that we know that the gravitational force in the numerator and then the separation is in the denominator with exponent two.
00:41
This shows an inverse square relationship.
00:44
So in symbols, i'd write here one over the square of r.
00:49
Again, this is an inverse relationship, inverse square relationship between gravitational force and separation.
00:58
So what does this mean? with the presence of exponent 2 here, we can immediately eliminate option a because option a shows a linear function, whereas the relationship here is we have an exponential relationship, particularly an exponential decay between fg and r.
01:21
So conceptually, if we have two masses that are separated by distance are initially and the gravitational force between them initially is f sub g then if we double the the separation between them in doing the inverse square relationship we get the inverse of factor two here so the inverse of two is one is one half and then we square it so this will now be the factor of the gravitational force in other words doubling the separation will make the gravitational force decrease by one -fourth the original...