Question

Two identical satellites $A$ and $B$ revolve around the earth in circular orbits at distance $R$ and $3R$ from the surface of the earth. The ratio of the linear momenta of $A$ and $B$ is ($R$ = radius of the earth)

• A. $1 : 1$
• B. $1 : \sqrt{2}$
• C. $\sqrt{2} : 1$
• D. $2 : 1$

Answer 1

Answer: (C)

$\sqrt{2} : 1$

Answer 2

Linear momentum of satellite, $p = m \upsilon_0 = m \sqrt{GM/ r} \:\:\: i.e, \, p \propto 1 /\sqrt{r} ;$ $\therefore \, \frac{p_A}{p_B} = \sqrt{\frac{r_B}{r_A}} = \sqrt{\frac{ R+3R}{R+R}} = \sqrt{2}$