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 `36 m` to `45 m`?

Answer 1

`1.03*10^-23J`

Explanation:

`m_1=4MG=4*10^-6 kg`
`m_2=7 MG=7*10^-6 kg`
`"Potential Energy"=-(Gm_1m_2)/r`
when `r=36m`
Potential Energy is `U_1=-(Gm_1m_2)/36`
when `r=45m`
Potential Energy is `U_2=-(Gm_1m_2)/45`

Change in Gravitational Potential Energy `=U_2-U_1`
`=-(Gm_1m_2)/45-(-(Gm_1m_2)/36)`
`=-(Gm_1m_2)/45+(Gm_1m_2)/36`
`=Gm_1m_2(1/36-1/45)`
`=6.67*10^-11(4*10^-6)(7*10^-6)((45-36)/(45*36))`
`=6.67*28*10^-23((9)/(45*36))`
`=186.76*10^-23((1)/(180))`
`=1.03*10^-23 J`