Question

Given that the mass and the radius of the planet are four times and one-ninth that of the earth respectively and the orbital velocity of an artificial satellite whose orbit is close to the surface of the earth is $7.92{kms}^{-1}$ , the orbital velocity of an artificial satellite orbiting around the planet close to its surface ____ ${kms}^{-1}$

• A. $12.11$
• B. $47.52$
• C. $36.4$
• D. $22.7$

Answer 1

The correct option is B $47.52$

$M_p=4M_e{R}_p=\frac{R_e}{9}{V}_e=\sqrt{\frac{G{M}_e}{R_e}}=7.92km{s}^{-1}{V}_p=\sqrt{\frac{G{M}_p}{R_p}}=\sqrt{\frac{G{4M}_e}{\frac{R_e}{9}}}=6\sqrt{\frac{G{M}_e}{R_e}}=47.52km{s}^{-1}$