Question

Two satellites $A$ and $B$ go round a planet $P$ in circular orbits having radii $4R$ and $R$ respectively. If the speed of the satellite $A$ is $3\upsilon$, the speed of satellite $B$ will be

• A. $12 \upsilon$
• B. $6 \upsilon$
• C. $(4/3)\upsilon$
• D. $(3/2)\upsilon$

Answer 1

Answer: (B)

$6 \upsilon$

Answer 2

Orbit speed of the satellite around the earth is $\upsilon = \sqrt{ \frac{ GM}{ r}}$ where, G = Universal gravitational constant M = Mass of earth r = Radius of the orbit of the satellite For satellite A $r_A = 4 R , v_A = 3V$ ${\upsilon}_A = \sqrt{ \frac{GM}{ r_A}}$ ...(i) For satellite B $r_B= R , v_ B =?$ ${\upsilon}_B = \sqrt{ \frac{GM}{ r_B}}$ ...(ii) Dividing equation (ii) by equation (i), we get $\therefore \, \, \, \, \frac{ {\upsilon}_B}{ {\upsilon}_A}= \sqrt{\frac{r_A}{r_B}}$ or ${\upsilon}_B = {\upsilon}_A \sqrt{\frac{ r_A}{ r_B}}$ Substituting the given values, we get $\upsilon_B = 3 V \sqrt{\frac{4R}{ R}} \, \, \,$ or $\, \, \, \upsilon_B = 6V$