Question

The escape velocity from the surface of earth of mass 'M' and radius 'R' is 've'. The escape velocity from the surface of a planet whose mass and radius are 3 times that of the earth, will be

Options

• 9 v_e

• v_e

• 3 v_e

• 12 v_e

Answer 1

v_e 

Explanation:

Given: M_p = 3M_e, R_p = 3R_e

(v_e) = `sqrt((2GM_e)/R_e)`

v_p = `sqrt((2GM_p)/R_p)`

∴ `v_p/v_e = sqrt((M_p xx R_e)/(R_p xx M_e)) = sqrt((3M_e xx R_e)/(3R_e xx M_e))` = 1

∴ v_p = v_e