JEE Mains · Physics · STD 11 - 7. gravitation
A spaceship of mass \(2 \times 10^4\,kg\) is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be \(......\) (if \(g =10\,m / s ^2\) and radius of earth \(=6400\,km\) )
- A \(11.2(\sqrt{2}-1)\,km / s\)
- B \(7.9(\sqrt{2}-1)\,km / s\)
- C \(8(\sqrt{2}-1)\,km / s\)
- D \(7.4(\sqrt{2}-1)\,km / s\)
Answer & Solution
Correct Answer
(C) \(8(\sqrt{2}-1)\,km / s\)
Step-by-step Solution
Detailed explanation
\(v _{\text {orbit }}=\sqrt{\frac{ GM }{ R }}=\sqrt{ gR }\) \(v _{\text {escape }}=\sqrt{\frac{2 GM }{ R }}=\sqrt{2 gR }\) \(\Delta v =(\sqrt{2}-1) \sqrt{ gR }=8(\sqrt{2}-1)\,km / s\)
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