Question

Escape velocity from a planet is v_e. If its mass is increased to 8 times and its radius is increased to 2 times, then a new escape velocity would be ______.

Options

• v_e

• `sqrt2`

• 2v_e

• `2 sqrt2  "v"_"e"`

Answer 1

Escape velocity from a planet is v_e. If its mass is increased to 8 times and its radius is increased to 2 times, then a new escape velocity would be 2v_e.

Explanation:

v_e = `sqrt((2"GM"_"e")/"R"_"e")`

M' = 8M, R' = 2R

`"v"_"e"^("''") = sqrt((2 "G" (8"M"))/(2"R"))`

`"v"_"e"^("''")` = 2v_e