Question

Two satellites of masses $m_1$ and $m_2$ $(m_1>m_2)$ are revolving around the earth in a circular orbit of radii $r_1$ and $r_2$ $(r_1>r_2)$, respectively. Which of the following statements is true regarding their speeds ${\nu }_1$ and ${\nu }_2$

• A. $({\nu }_1={\nu }_2)$
• B. $({\nu }_1>{\nu }_2)$
• C. $({\nu }_1<{\nu }_2)$
• D. $\frac{{\nu }_1}{r_1}=\frac{{\nu }_2}{{\nu }_2}$

Answer 1

Answer: (C)

$({\nu }_1<{\nu }_2)$

From, $\frac{m{v}^2}{r}=\frac{GMm}{r^2}⟹v^2=\frac{GM}{r}⟹v^2\propto \frac{1}{r}$

Thus, as $r_1>r_2$ gives $v_2^2>v_1^2$

$⟹v_2>v_1$