Question

What is the minimum energy required to launch a satellite of mass 'm' from the surface of the earth of mass 'M' and radius 'R' at an altitude 2R?

Options

• `"GMm"/"2R"`

• `"2GMm"/"3R"`

• `"GMm"/"3R"`

• `"5GMm"/"6R"`

Answer 1

`"2GMm"/"3R"`

Explanation:

The minimum energy required to launch a satellite from surface of earth is equal to the amount of work done against gravity to move it from the surface of earth to a height hand Is given by

U = W = `"GMm" (1/"r"_1 - 1/"r"_2)`

`= "GMm" (1/"R" - 1/("R + h"))`

Here, h = 2R

`=> "U" = "GMm"(1/"R" - 1/"3R") = "2GMm"/"3R"`