Question

Two objects have masses of `5 MG` and `8 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `140 m` to `160 m`?

Answer 1

Change in Gravitational potential energy is `3.4541\times 10^(-24) J`

Explanation:

Gravitational potential energy is given by,

`U=−(Gm1m2)/r`

Given that,
`m1=5mg=5×10^-6` kg

`m2=8mg=8×10^-6` kg

Initial distance between the objects = `r1=140m`

Final distance between the objects =`r2= 160 m`

We will calculate the change in gravitational potential energy as:

When
`r1= 140m`m

`U1 = −(Gm1m2)/(r1)`

And

When `r2 = 160m`'

`U2 =−(Gm1m2)/(r2)`

Change in Gravitational Potential Energy = `U2 -U1`

=`(−(Gm1m2)/(r2) )- (−(Gm1m2)/(r1))`

=`(−(Gm1m2)/(160) )- (−(Gm1m2)/(140))`

=`(−(7Gm1m2)/(1120) +(8Gm1m2)/(1120))`

=`(Gm1m2)/(1120)`

Substitute the values of `G, m1 and m2`:

`U2- U1 = (6.67\times 10^(-11) \times 5×10^-6 \times 8×10^-6)/1120`

`U2- U1 = (386.86\times 10^(-11) \times10^-6 \times 10^-6)/1120 J`

`U2- U1 = (0.34541\times 10^(-11) \times 10^-6 \times 10^-6) J`

`U2- U1 = (0.34541\times 10^(-23) J`

`U2- U1 = 3.4541\times 10^(-24) J`

So, Change in Gravitational potential energy is `3.4541\times 10^(-24) J`