Question

The velocity of a satellite moving in an orbit about earth at a distance equal to radius $R$ of earth will be :

• A. $\sqrt{gR}$
• B. $\sqrt{0.5gR}$
• C. $\sqrt{2gR}$
• D. $\sqrt{3gR}$

Answer 1

Answer: (B)

$\sqrt{0.5gR}$

Let the mass of satellite be $m$ and velocity be $v$.

As the distance from the earth surface is $R$, the distance from the center of earth is, $R+R=2R$

The gravitational force due to earth is, $F_g=GMm/(2R{)}^2=mg/4$, towards the center.

As satellite is in circular motion around the earth, the centripetal force equals the gravitational pull towards the earth.

$\therefore m{v}^2/\left(2R\right)=mg/4⟹v=\sqrt{0.5gR}$