Question

A satellite is revolving round the earth in an orbit of radius $r$ with time period $T$. If the satelite is revolving round the earth in an orbit of radius $r+△r(△r<<r)$ with time period $T+△T$ then,

• A. $\frac{△T}{T}=\frac{3}{2}\frac{△r}{r}$
• B. $\frac{△T}{T}=\frac{2}{3}\frac{△r}{r}$
• C. $\frac{△T}{T}=\frac{△r}{r}$
• D. $\frac{△T}{T}=-\frac{△r}{r}$

Answer 1

Answer: (A)

$\frac{△T}{T}=\frac{3}{2}\frac{△r}{r}$

Since, $T^2=k{r}^3$
Differentiating the above equation
$\Rightarrow 2\frac{△T}{T}=3\frac{△r}{r}\Rightarrow \frac{△T}{T}=\frac{3}{2}\frac{△r}{r}$