An asteroid of mass `m` is approaching earth, initially at a distance `10R_(E)` with speed `v_(i)`. It hits earth with a speed `v_(f)` (`R_(E)` and `M_(E)` are radius and mass of earth),. Then

Options

A. `v_(f)^(2)=v_(i)^(2)+(2Gm)/(M_(e)R)(1-1/10)`
B. `v_(f)^(2)=v_(i)^(2)+(2GM_(e))/(R_(e))(1+1/10)`
C. `v_(f)^(2)=v_(i)^(2)+(2GM_(e))/(R_(e))(1d-1/10)`
D. `v_(f)^(2)=v_(i)^(2)+(2Gm)/(R_(e))(1-1/10)`

Answer

C

Explanation

Using conservation of enerty
`1/2mv_(i)^(2)=(GM_(e)m)/(10R_(e))=1/2mv_(r)^(2)-(GM_(e)m)/R`
`v_(f)^(2)=v_(i)^(2)+(2GM_(e))/R(1-1/10)`