Question

An asteroid of mass m is approaching earth, initially at a distance 10 with speed It hits earth with a speed ( and are radius and mass of earth). Then

• A. $\mathrm { v } _ { \mathrm { f } } ^ { 2 } = \mathrm { v } _ { \mathrm { i } } ^ { 2 } + \frac { 2 \mathrm { Gm } } { \mathrm { R } _ { \mathrm { E } } } \left( 1 + \frac { 1 } { 10 } \right)$
• B.
• C.
• D. $\mathrm { v } _ { \mathrm { f } } ^ { 2 } = \mathrm { v } _ { \mathrm { i } } ^ { 2 } + \frac { 2 \mathrm { Gm } } { \mathrm { R } _ { \mathrm { E } } } \left( 1 - \frac { 1 } { 10 } \right)$

Answer 1

Answer: (C)

Answer 2

Initial energy of the asteroid is

Final energy of the asteroid is

According to law of conservation of energy,

$\frac { 1 } { 2 } \mathrm { mv } _ { \mathrm { i } } ^ { 2 } - \frac { \mathrm { GM } _ { \mathrm { E } } \mathrm { m } } { 10 \mathrm { R } _ { \mathrm { E } } } = \frac { 1 } { 2 } \mathrm { mv } _ { \mathrm { f } } ^ { 2 } - \frac { \mathrm { GM } _ { \mathrm { E } } \mathrm { m } } { \mathrm { R } _ { \mathrm { E } } }$