Question

Two objects have masses of `32 MG` and `35 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `4 m` to `24 m`?

Answer 1

Change in Gravitational Potential Energy=`1.5563\ times 10^(-20)J`

Explanation:

Gravitational potential energy is given by,

`U = - \frac{Gm1m2}{r}`

Given that,
`m1 = 32mg = 32\times 10^(-6) kg`
`m2 = 35mg = 35\times 10^(-6)kg`
Initial distance between the objects = `r = 4m`
Final distance between the objects =`r= 24m`

We will calculate the change in gravitational potential energy as:

When `r= 4m`,

`U1 = - \frac{Gm1m2}{4m}`

when `r = 24m`,

`U2 = - \frac{Gm1m2}{24}`

Change in Gravitational Potential Energy = `U2- U1`

=`(- \frac{Gm1m2}{24} ) - ( - \frac{Gm1m2}{4})`

=`(- \frac{Gm1m2}{24} + \frac{Gm1m2}{4})`

=`Gm1m2(- \frac{1}{24} + \frac{1}{4})`

=`Gm1m2(- \frac{1}{24} + \frac{1}{4}(6/6))`

=`Gm1m2(\frac{-1+6}{24} )`

=`Gm1m2(\frac{5}{24} )`

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

=`6.67\times 10^(-11)\times 32\times 10^(-6) kg\ times35\times 10^(-6)kg\ times(5/24)`

`= 6.67\times32\times35\times(5/24)\times10^(-11-6-6)`

`=6.67\times (5600/24)\times10^(-23)`

=`1556.333\times 10^(-23) J`

=`1.5563\ times 10^(-20)J`