Question

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?

Answer 1

(a) No

(b) No

(c) No

(d) Yes

Escape velocity of a body from the Earth is given by the relation:

`v_"esc" = sqrt(2gR)`   ...i

g = Acceleration due to gravity

R = Radius of the Earth

It is clear from equation (i) that escape velocity v_esc is independent of the mass of the body and the direction of its projection. However, it depends on gravitational potential at the point from where the body is launched. Since this potential marginally depends on the height of the point, escape velocity also marginally depends on these factors.

Answer 2

The escape speed `v_es` = `sqrt((2GM)/R)` = `sqrt2gR`. Hence

(a) The escape speed of a body from the Earth does not depend on the mass of the body.

(b) The escape speed does not depend on the location from where a body is projected.

(c) The escape speed does not depend on the direction of projection of a body.

(d) The escape speed of a body depends upon the height of the location from where the body is projected, because the escape velocity depends upon the gravitational potential at the point from which it is projected and this potential depends upon height also