Question

If a graph is plotted between $T^{2}and{r}^3$ for a planet then its slope will be.

• A. $\frac{4{\pi }^2}{GM}$
• B. $\frac{GM}{4{\pi }^2}$
• C. $4\pi Gm$
• D. zero

Answer 1

Answer: (A)

$\frac{4{\pi }^2}{GM}$

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

Thus $T^2=\frac{4{\pi }^2}{GM}{r}^3$

Hence slope will be $\frac{4{\pi }^2}{GM}$