A space ship of mass 2 × 10 4   kg is launched into a circular orbit close to the earth surface.…

A space ship of mass 2×104 kg is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if g=10 m s-2 and radius of earth =6400 km ):
  1. 11.2(2-1) km s-1
  2. 8(2-1) km s-1
  3. 7.9(2-1) km s-1
  4. 7.4(2-1) km s-1

Solution

 The orbital velocity of satellite is 

vorb=GMR

The escape velocity is 

vesc=2GMR

Hence, the additional velocity required is 

Δv=vesc-vorb=2GMR-GMR=(2-1)GMR
=(2-1)gR
=(2-1)10×6400×103
=8(2-1) km s-1

Asked in: JEE Main 2023 (11 Apr Shift 2)

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