Question

A planet of mass m and radius r is surrounded by an atmosphere of constant density. The atmosphere consists of an ideal gas of molar mass M and its thickness (radial) is h (h << r) from the surface. The temperature of the atmosphere on the surface of the planet is [R = universal gas constant]

• A. $\frac{mGMh}{R{r}^2}$
• B. $\frac{2mGMh}{R{r}^2}$
• C. $\frac{3mGMh}{R{r}^2}$
• D. $\frac{4mGMh}{R{r}^2}$

Answer 1

The correct option is A

$\frac{mGMh}{R{r}^2}$

$P=\rho \left(\frac{Gm}{r^2}\right)handPM=\rho RT\Rightarrow T=\frac{mGMh}{R{r}^2}$