Question

The orbital velocity of earths satellite near surface is 7 km/s. When the radius of orbit is 4 times than that of earths radius. Then orbital velocity in that orbit will be :

• A. 7 km/s
• B. 3.5 km/s
• C. 5.2 km/s
• D. 9.4 km/s

Answer 1

Answer: (B)

From the formula, the orbital velocity is ${\upsilon }_0=\frac{\sqrt{GM}}{R}=7km/\sec$ ?..(1) If the radius of the orbit is four times that of the earth, then we have ${\upsilon }_0^{}=\frac{\sqrt{GM}}{4R}$ ...(2) Now from equation (1) and (2) we get $\frac{7}{{\upsilon }_0^{}}=\frac{\sqrt{GM/R}}{\sqrt{GM/4R}}=\frac{2}{1}$ So, ${\upsilon }_0^{}=\frac{7}{2}=3.5km/s$