Ncert Exercises & Solutions

8.7 Does the escape speed of a body from the earth depend on (a) the mass of the body, (b) the location from where it is projected, (c) the direction of projection, (d) the height of the location from where the body is launched?

(a) No

(b) No

(d) Yes

We know that,

$v_{e} = \sqrt{2 gR}$

g = Acceleration due to gravity

R = Radius of the Earth

So we can say that escape velocity $v_{e}$ is independent of the mass of the body and the direction of its projection. However, it depends on the gravitational potential at the point where the body is launched. Since this potential marginally depends on the height of the point, escape velocity also marginally depends on these factors.

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