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 $10^{-34} yr ^{2} m ^{-3}$ is approximately

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

Answer 1

Answer: (A)

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