A) 2.5 km/s
B) 0.14 km/s
C) 5 km/s
D) 8 km/s
Correct Answer: A
Solution :
At a certain velocity of projection the body will go out of the gravitational field of the earth and will never return to earth. This initial velocity is called escape velocity \[\frac{1}{F}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}\] ?..(1) where \[{{f}_{1}}=40cm,{{f}_{2}}=-25cm\] is mass of earth, \[=\frac{100}{F}=-\frac{300}{200}=-1.5D\] is radius and G is gravitational constant. At moon, \[\propto \] Given, \[\propto \] \[H={{i}^{2}}Rt\] \[\Rightarrow \] ?.(2) Dividing Eq. (1) by Eq. (2), we get \[\propto \] \[\frac{1}{R}=\frac{1}{R}+\frac{1}{R}=\frac{2}{R}\] \[H\propto \frac{R}{2}\] \[R=R+R=2R\] \[\mu \propto 2R\] Note: As moon has very less escape velocity, so that root mean square velocity of gas molecules at moon is greater than their escape velocity and hence, they escape moons gravitational field. Hence, moon has no atmosphere,
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