Question

If a plant of mass $m$ is revolving around the sun in a circular orbit of radius $r$ with time period $T$ , then mass of the sun is the

• A. $4{\pi }^2{r}^3/GT$
• B. $4{\pi }^2{r}^3/G{T}^2$
• C. $4{\pi }^{2}r/GT$
• D. $4{\pi }^2{r}^3/G^2{T}^2$

Answer 1

The correct option is B $4{\pi }^2{r}^3/G{T}^2$

Gravitational force

$=G\frac{MsM}{R^2}$

centripetal force $=MRc$

$\therefore w=\frac{2\pi }{T}$

$G\frac{MsM}{R^2}=MR{\left(\frac{2\pi }{T}\right)}^2$

$G\frac{Ms}{R^2}=R\left(\frac{4{\pi }^2}{T^2}\right)$

$Ms=\frac{R^3}{G}\left(\frac{4{\pi }^2}{T^2}\right)$