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Q.
A satellite is orbiting close to the earth and has a kinetic energy K. The minimum extra kinetic energy required by it to just overcome the gravitation pull of the earth is
We know $v_{e}=\sqrt{2} v_{0}$
When satellite is in orbit $K=\frac{1}{2} mv_{0}^{2}$
For satellite to escape its velocity should be $v_{e}$
$\therefore \, $ K.E. To escape, $K_{e}=\frac{1}{2} m v_{e}^{2}=\frac{1}{2} m \left(\sqrt{2}v_{0}\right)^{2}=2k$
$\therefore \, $ Extra K.E. required=2K-K=K