A satellite is revolving around the earth, close to the surface of earth with a kinetic energy E. How much kinetic energy should be given to it so that it escapes from the surface of earth

A satellite is reducing closer to earth surface                 

$\text{K}{\text{.E}}_{\text{initial}}=\text{E}$

$\frac{1}{2}{\text{mv}}_{\text{i}}^{\text{2}}=\text{E}$

$\therefore \frac{1}{2}{\text{mv}}^{\text{2}}=\frac{\text{GMm}}{\text{2R}}\Rightarrow \frac{\text{GMm}}{\text{2R}}=\text{E}$

$\text{P}{\text{.E}}_i=\frac{-\text{GMm}}{\text{R}}=-\text{2E}$

$\text{T}{\text{.E}}_{\text{initial}}=\text{K}{\text{.E}}_{\text{i}}+\text{P}{\text{.E}}_i$

$\text{T}{\text{.E}}_{\text{i}}=\text{E}-\text{2E}=-\text{E}$

To make it escape from the earth, the K.E required to make as zero $\text{T}{\text{.E}}_{\text{i}}$ will be

$\frac{1}{2}{\text{mv}}^{\text{2}}+\text{T}{\text{.E}}_{\text{i}}\ge 0$

$\text{K}{\text{.E}}_{\text{f}}-\text{E}=0$

$\text{K}{\text{.E}}_{\text{f}}=\text{E}$