Question

Two objects have masses of `9 MG` and `12 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `50 m` to `230 m`?

Answer 1

`1.1275*10^-22J`

Explanation:

`m_1=9MG=9*10^-6 kg`
`m_2=12 MG=12*10^-6 kg`
`"Potential Energy"=-(Gm_1m_2)/r`
when `r=50m`
Potential Energy is `U_1=-(Gm_1m_2)/50`
when `r=230m`
Potential Energy is `U_2=-(Gm_1m_2)/230`

Change in Gravitational Potential Energy `=U_2-U_1`
`=-(Gm_1m_2)/230-(-(Gm_1m_2)/50)`
`=-(Gm_1m_2)/230+(Gm_1m_2)/50`
`=Gm_1m_2(1/50-1/230)`
`=6.67*10^-11(9*10^-6)(12*10^-6)((230-50)/(50*230))`
`=6.67*9*12*10^-23((180)/(50*230))`
`=11.275*10^-23J`
`=1.1275*10^-22J`