Question

Two planets A and B have radii R and R/n^2 the ratios of the time periods of their revolution is
a) 1/n^2
b) n^2
c) 1/n^3
d) n^3
may i get the right answer please ??​

Answer 1

The ratios of the time periods of their revolution is n³

(d) is correct option

Explanation:

Given that,

Radius of plate A $r_{A} = R$

Radius if plate B $r_{B}=\dfrac{R}{n^2}$

We need to calculate the ratios of the time periods of their revolution

Using Kepler's third law

$(\dfrac{T_{A}}{T_{B}})^2=(\dfrac{r_{A}}{r_{B}})^3$

Put the value into the formula

$\dfrac{T_{A}^2}{T_{B}^2}=\dfrac{R^3}{\dfrac{R^3}{n^6}}$

$\dfrac{T_{A}}{T_{B}}=\sqrt{\dfrac{R^3\times n^6}{R^3}}$

$\dfrac{T_{A}}{T_{B}}=n^3$

Hence, The ratios of the time periods of their revolution is n³

Learn more :

Topic : Kepler's law

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