Question

Two objects have masses of `4 MG` and `7 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `320 m` to `450 m`?

Answer 1

Change in gravitational potential energy
`=1.69xx10^-6J` rounded to two decimal places

Explanation:

Gravitational potential energy `PE_g` between two objects of masses `m_1 and m_2` is given by the relation

`PE_g = − (Gm_1m_2)/r`,
where `r` is the separation between their centres and `G` is the universal gravitational constant (`6.67 xx 10^(−11) m^3 kg^-1 s^-1`)

As the distance between their centres changes from `r_I=320m` to `r_F=450m`, the change in gravitational potential energy can be found from
`Delta PE_g=− (Gm_1m_2)/r_F-(− (Gm_1m_2)/r_I)`
`=− (Gm_1m_2)[1/r_F-1/r_I]`
Inserting the given values, mass `1Mg=10^3kg`
`=-(6.67 xx 10^(−11)xx4xx10^3xx7xx10^3)[1/450-1/320]`
or `=-(186.76 xx 10^(−5))xx(-9.02 dot7xx10^-4)`
`=1.69xx10^-6J` rounded to two decimal places