Question

The orbital velocity of a satellite revolving near a planet is.

• A. directly proportional to density of planet
• B. directly proportional to square root of density of
  planet
• C. directly proportional to cube of density of planet
• D. directly proportional to square of density of planat

Answer 1

The correct option is B directly proportional to square root of density of

planet
Orbital velocity, $v=\sqrt{\frac{GM}{r}}$ where r is the orbital radius and M is the mass of planet.

Now let density of planet be $\rho$

Thus, $M=\rho \times \frac{4}{3}\pi R^3$ where R is the radius of the planet

$⟹v=\sqrt{\frac{\rho G\times \frac{4}{3}\pi R^3}{r}}$

Hence, $v\propto \sqrt{\rho }$