NEET Sample Paper NEET Sample Test Paper-15

  • 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)  R

    C)  3R                  

    D)  6R

    Correct Answer: B

    Solution :

    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].

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