Orbital Velocity

NCERT Class 11, Chapter 8 (Gravitation) shows that orbital speed depends on orbit radius through $v_o=\sqrt{\frac{GM}{r}}$, obtained by balancing the gravitational pull against the centripetal requirement of circular motion. The key feature is that $v_o\propto \frac{1}{\sqrt{r}}$, so a satellite in a larger orbit actually moves more slowly, which can seem counter-intuitive. Taking the ratio for the two satellites, $\frac{v_1}{v_2}=\sqrt{\frac{r_2}{r_1}}=\sqrt{\frac{4}{1}}=2$, giving $v_1:v_2=2:1$. The option $1:2$ inverts the dependence, wrongly suggesting the inner satellite is the slower one. The option $4:1$ treats speed as inversely proportional to radius itself, ignoring the square root. The option $1:4$ both inverts the relationship and drops the root. As a plausibility check, the inner satellite sits where gravity is stronger and must travel faster to remain in a stable circle, so a speed ratio greater than one for the inner-to-outer pairing is physically correct, and the value of two follows directly from the square-root law.