Question

A particle is kept at rest at a distance R (Earth's radius) above the earth's surface. The minimum speed with which it should be projected so that it does not return is :

• A. $\sqrt { \frac { \mathrm { GM } } { 4 \mathrm { R } } }$
• B. $\sqrt { \frac { \mathrm { GM } } { 2 \mathrm { R } } }$
• C. $\sqrt { \frac { \mathrm { GM } } { \mathrm { R } } }$
• D. $\sqrt { \frac { 2 \mathrm { GM } } { \mathrm { R } } }$

Answer 1

Answer: (C)

$\sqrt { \frac { \mathrm { GM } } { \mathrm { R } } }$

Answer 2

using conservation of energy

– + $\frac { 1 } { 2 }$ mv² = 0

or mv² =

or v = $\sqrt { \frac { \mathrm { GM } } { \mathrm { R } } }$