In a two stage launch of a satellite, the first stage brings the satellite to a height of 150 km and the 2^(nd) stage gives it the necessary criticalspeed to put it in a circular orbit. Which stage requires more expenditure of fuel? Given mass of earth =6.0xx10^(24)kg radius of earth =6400 km.

In a two stage launch of a satellite, the first stage brings the satel

1.	In a two stage launch of a satellite, the first stage brings the satellite to a height of 150 km and the 2^(nd) stage gives it the necessary criticalspeed to put it in a circular orbit. Which stage requires more expenditure of fuel? Given mass of earth =6.0xx10^(24)kg radius of earth =6400 km.
Answer» Solution :Work done on SATELLITE in first state `=W_(1)=PE` at 150 km -PE at the surface `W_(1)= (GMm)/(R+h)-(-(GMm)/(R ))` `=(GMmh)/(R(R+h))` Work done on satellite in `2^(nd)" stage "W_(2)` = energy REQUIRED to GIVE orbital VELOCITY `v_(0)` `=(1)/(2)mv_(0)^(2)= (1)/(2)((GMm)/(R+h))` `(W_1)/(W_2)=(2h)/(R )= (2xx150)/(6400)= (3)/(64) lt 1` `W_2 gt W_1`, so second stage require more energy.