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A particle is taken to a distance \( \mathrm{r}(\mathrm{R}) \) from centre of the earth. \( \mathrm{R} \) is radius of the earth. It is given velocity \( \mathrm{V} \) which is perpendicular to \( \vec{r} \). With the given values of \( \mathrm{V} \) in column I you have to match the values of total energy of particle in column II and the resultant path of particle in column III. Here ' \( \mathrm{G} \) ' is the universal gravitational constant and 'M' is the mass of the earth.
Column I(Velocity) Column II (Total energy) Column III (Path)
(A) \( \mathrm{V}=\sqrt{\mathrm{GM} / \mathrm{r}} \)
(p) Negative
(t) Elliptical
B) \( V=\sqrt{2 \mathrm{GM} / \mathrm{r}} \)
(q) Positive
(u) Parabolic
(C) \( \mathrm{V}\sqrt{2 \mathrm{GM} / \mathrm{r}} \)
(r) Zero
(v) Hyperbolic
D) \( \sqrt{\mathrm{GM} / r}\mathrm{V}\sqrt{2 \mathrm{GM} / r} \)
(s) Infinite
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