Question

Two satellites of masses $m_1$ and $m_2$($m_1$> $m_2$) are revolving round the earth in circular orbits of radii $r_1$ and $r_2$($r_1$> $r_2$) respectively. Which of the following statements is true regarding their speeds $v_1$ and $v_2$$v_1$?

• A. $v_1$ = $v_2$
• B. $v_1$ $>$ $v_2$
• C. $v_1$ $<$ $v_2$
• D. $\frac{v_1}{r_1}=\frac{v_2}{r_2}$
  

Answer 1

Answer: (C)

$v_1$ $<$ $v_2$

consider a satellite revolving at a distance r from the earth.

inward force is $\frac{GMm}{r^2}$

and outward force is $\frac{m{v}^2}{r}$

equating both the expression for equilibrium.

so $v=\sqrt{\frac{GM}{r}}$.

so to if $r$ increses then $v$ decrease.

so best possible answer is option C.