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Physics Question on Newtons law of gravitation

The mass of a spaceship is 1000 kg1000 \,kg. It is to be launched from the earth's surface out into free space. The value of gg and RR (radius of earth) are 10 m/s210\, m/s^2 and 6400 km6400\, km respectively. The required energy for this work will be :

A

6.4??10116.4 ??10^{11} Joules

B

6.4??1086.4 ??10^{8} Joules

C

6.4??1096.4 ??10^{9} Joules

D

6.4??10106.4 ??10^{10} Joules

Answer

6.4??10106.4 ??10^{10} Joules

Explanation

Solution

W=0−(−GMmR)=GMmRW=0-\left(-\frac{GMm}{R}\right)=\frac{GMm}{R} =gR2×mR=mgR=gR^{2}\times \frac{m}{R}=mgR =1000??10??6400??103= 1000 ??10 ??6400 ??10^{3} =64??109 J= 64 ??10^{9}\, J =64??1010= 64 ??10^{10}