Question

Two satellites of mass $m$ and $2m$ are revolving in two circular orbits of radii $r$ and $2r$ around an imaginary planet, on the surface of with gravitational force is inversely proportional to distance from its centre. The ratio of orbital speed of satellite is :

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

Answer 1

The correct option is A $1:1$

from the figure, centripetal force,

$f=\frac{m{v}^2}{r}$

$v^2=\frac{fr}{m}$

The orbital speed of 1st satellite is

$v_1=\sqrt{\frac{fr}{m}}$. . . .(1)

The orbital speed of 2nd satellite,

$v_2=\sqrt{\frac{f2r}{2m}}$

$v_2=\sqrt{\frac{fr}{m}}$. . . . .(2)

Ratio $v_1:v_2=1:1$

The correct option is A.