A) \[\frac{r}{v}{{\left[ {{v}^{2}}+\frac{2GM}{r} \right]}^{\frac{1}{2}}}\]
B) \[\operatorname{vr}\left[ 1+\frac{2GM}{r} \right]\]
C) \[\frac{r}{v}\left[ {{v}^{2}}+\frac{2GM}{r} \right]\]
D) \[\frac{2GMv}{r}\]
Correct Answer: A
Solution :
[a] From the principle of conserving angular momentum, we have \[MvR=mv'r\] ...(i) [\[v'=\]speed when spaceship is just touching the plane] From conserving of energy, we have \[\frac{1}{2}m{{v}^{2}}=\frac{1}{2}mv{{'}^{2}}-\frac{GMm}{r}\] ?.(ii) Solving Eqs. (i) and (ii), we get \[R=\frac{r}{v}{{\left[ {{v}^{2}}+\frac{2GM}{r} \right]}^{1/2}}\]
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