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_eR)(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)(1-(1)/(10))`
D. `v_f^2=v_i^2+(2Gm)/(R_e)(1-(1)/(10))`

Answer

C

Explanation

Law of conservation of energy
`(-GMm)/(10R_e)+1/2mv_i^2=(-GMm)/(R_e)+1/2mv_f^2`
`v_f^2=v_i^2-(GM_e)/(5R_e)+(2GM)/(R_e)`
`rArrv_f^2=v_i^2+(2GM)/(R_e)(1-1/10)`