Question

An artificial satellite of mass M & radius $R$ is revolving in a circular orbit of radius $r$. $g$ is acceleration due to gravity. Time period of revolution is ($K$ is a dimensionless unit)

• A. $T=\frac{K}{R}\sqrt{\frac{r^3}{g^2}}$
• B. $T=\frac{K}{R}\sqrt{\frac{r^3}{g}}$
• C. $T=\frac{K}{R^2}\sqrt{\frac{r^3}{g}}$
• D. $T=\frac{K}{R^3}\sqrt{\frac{r^4}{g^2}}$

Answer 1

The correct option is B $T=\frac{K}{R}\sqrt{\frac{r^3}{g}}$

Dimension must be same on both the sides.