An asteroid of mass m is approaching earth, initially at a distance of 10 R_e with speed v_i. It hits the earth with a speed v_f (R_e and M_e are radius and mass of earth), then :

• A

  ${\mathrm{v}}_{\mathrm{f}}^2={\mathrm{v}}_{\mathrm{i}}^2+\frac{2\mathrm{Gm}}{{\mathrm{M}}_{\mathrm{e}}\mathrm{R}}\left(1-\frac{1}{10}\right)$

• B

  ${\mathrm{v}}_{\mathrm{f}}^2={\mathrm{v}}_{\mathrm{i}}^2+\frac{2{\mathrm{GM}}_{\mathrm{e}}}{{\mathrm{R}}_{\mathrm{e}}}\left(1+\frac{1}{10}\right)$

• C

  ${\mathrm{v}}_{\mathrm{f}}^2={\mathrm{v}}_{\mathrm{i}}^2+\frac{2{\mathrm{GM}}_{\mathrm{e}}}{{\mathrm{R}}_{\mathrm{e}}}\left(1-\frac{1}{10}\right)$

• D

  ${\mathrm{v}}_{\mathrm{f}}^2={\mathrm{v}}_{\mathrm{i}}^2+\frac{2\mathrm{Gm}}{{\mathrm{R}}_{\mathrm{e}}}\left(1-\frac{1}{10}\right)$