There are two planets. The ratio of the radii of the two planets is $K$,and the ratio of the acceleration due to gravity of both planets is $g$. What will be the ratio of their escape velocities?
- A$(Kg)^{1/2}$
- B$(Kg)^{-1/2}$
- C$(Kg)^2$
- D$(Kg)^{-2}$
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The escape velocity of an object from the Earth depends upon the mass of the Earth $(M)$,its mean density $(\rho)$,its radius $(R)$,and the gravitational constant $(G)$. Thus,the formula for escape velocity is:
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Match Column-$I$ with Column-$II$.
Column-$I$ Column-$II$ $(1)$ Value of escape velocity on the surface of the Earth $(a)$ $2.38 \, km \, s^{-1}$ $(2)$ Value of escape velocity on the surface of the Moon $(b)$ $7.92 \, km \, s^{-1}$ $(c)$ $11.2 \, km \, s^{-1}$
| Column-$I$ | Column-$II$ |
|---|---|
| $(1)$ Value of escape velocity on the surface of the Earth | $(a)$ $2.38 \, km \, s^{-1}$ |
| $(2)$ Value of escape velocity on the surface of the Moon | $(b)$ $7.92 \, km \, s^{-1}$ |
| $(c)$ $11.2 \, km \, s^{-1}$ |
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