The gravitational potential energy of a rocket of mass 200kg at a height of `10^(7)`m from the earth's surface is `10^(9)`s. The potential energy of the rocket at a height of `26.4xx10^(6)`m from the surface of earth is:

Options

A. `-1.5xx10^(9)J`
B. `-0.5xx10^(9)J`
C. `-2.5xx10^(9)J`
D. `-2xx10^(9)J`

Answer

B

Explanation

`U=-(GMm)/((R+h))" "U'=-(GMm)/((R+h'))`
`(U')/(U)=((R+h)/(R+h'))`
`=((6.4+10)xx10^(6))/((6.4+26.4)xx10^(6))`
`=(16.4)/(32.8)=(1)/(2)`
`thereforeU'=-(U)/(2)=(-10^9)/(2)=-0.5xx10^(9)J`