Question

A spaceship is launched into a circular orbit close to earth's surface. What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull? (Radius of earth =6400 km and g = 9.8 ${m/s}^2$)

• A. 2.83km/s
• B. 3.28 km/s
• C. 6.68 km/s
• D. 8.32 km/s

Answer 1

The correct option is B 3.28 km/s

Orbit velocity spaceship ,
$v_0=\sqrt{\frac{GM}{r}}(\because r>>R)Since,g\sqrt{\frac{GM}{R^2}},\therefore GM=g{R}^{2}Now{v}_0=\sqrt{Rg}=\sqrt{6.4\times {10}^6\times 9.8}=7.9195km/sAgain{v}_e=\sqrt{2Rg}=\sqrt{2\times 7.9195}=11.20km/s\therefore Additionalvelocityrequired=11.20-7.9195=3.28km/sec$