Question

The mass of a spaceship is 1000kg . it is to be launched from the earth's surface out into free space . the value of g and R (radius of earth ) are 10 m/s² and 6400 km , respectively . the required energy for this work will be . ​

Answer 1

Explanation:- Potential energy on earth surface is - mgR while in free space , it is zero . so to free the spaceship minimum required energy is

• ∵ PE = - GmM /R

• but , g = GM/R²
• G = gR²/M

∴ PE = - gR²m M / MR= -gmR

now, given that , mass of spaceship 1000kg = 10³ kg , g = 10m/s² , R = 6400km = 6400× 10³ m

• K = 10³ × 10× 6400 × 10³ J
• K = 6.4 × 10¹⁰ J Answer

minimum energy required is 6.4× 10¹⁰J