Question

The time period of revolution $T$ of planet in years (yr) is 84. The semi-major axis $a$ in units of $10^{10}m$ is 287 . The quotient $\left(T^2/a^3\right)$ in units of $10^{-34}y{r}^2{m}^{-3}$ is approximately

• A. 3 units
• B. 4 units
• C. 2 units
• D. 1 unit

Answer 1

Answer: (A)

Given, time period of revolution, $T=84yr$,
Semi-major axis, $a=287\times 10^{10}m$
Then, $[\frac{T^2}{a^3}=\frac{(84{)}^2}{{\left(287\times 10^{10}\right)}^3}=2.98\times 10^{-34}y{r}^2{m}^{-3}$
$\approx 3.00\times 10^{-34}y{r}^2{m}^{-3}$
Thus, the quotient $\left(T^2/a^3\right)$ in units of $10^{-34}y{r}^2{m}^{-3}$ is approximately $3$ units.