Question

A satellite is launched into a circular orbit of radius $r$ while a second satellite is launched into an orbit of radius $1.02r$. The percentage difference in the time periods of the two satellites is:

• A. $0.7$
• B. $1.0$
• C. $1.5$`
• D. $3.0$

Answer 1

The correct option is D $3.0$

Time period $T=2\pi \sqrt{\frac{r^3}{GM}}$

So, percentage change in time period $\frac{\Delta T}{T}\times 100=\frac{3}{2}\times \frac{\Delta r}{r}\times 100$

Given : $\frac{\Delta r}{r}\times 100=\frac{1.02r-r}{r}\times 100=2$

$⟹$ $\frac{\Delta T}{T}\times 100=\frac{3}{2}\times 2=3$