Question

A spaceship is launched into a circular orbit of radius $R$ close to the surface of earth. The additional velocity to be imparted to the spaceship in the orbit to overcome the earth's gravitational pull is : $($ $g=$ acceleration due to gravity $)$

• A. $1.414Rg$
• B. $1.414\sqrt{Rg}$
• C. $0.414Rg$
• D. $0.414\sqrt{gR}$

Answer 1

Answer: (D)

$0.414\sqrt{gR}$

Velocity of the spaceship when in a circular orbit of radius $R=\sqrt{gR}$
where g is the acceleration due to gravity and $R$ is the radius of the earth .
Velocity needed to escape earth's gravitational pull $=\sqrt{2gR}$
$\therefore$ Additional velocity to be imparted $=\sqrt{2gR}-\sqrt{gR}$ $=(\sqrt{2}-1)\sqrt{gR}$