• # question_answer An artificial satellite is moving in a circular orbit around the earth with a speed equal to the escape velocity from the earth of radius R. What is the height of the satellite above the surface of the earth? A) $\frac{R}{2}$                       B)  RC)  3R                  D)  6R

Orbital speed ${{v}_{1}}=\sqrt{\frac{GM}{r}},$while escape velocity ${{v}_{c}}=\sqrt{\frac{2GM}{R}}$ But ${{v}_{0}}=\frac{1}{2}{{v}_{c}}$$\therefore$$\sqrt{\frac{GM}{r}}=\sqrt{\frac{GM}{r}}\Rightarrow r=2R$ $\therefore$Height above earth is $2R-R.$ Hence, the correction option is [b].