Which of the following quantities does not depends upon the orbital radius of the satellite?

\frac{T}{R}

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\frac{T^{2}}{R}

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\frac{T^{2}}{R^{2}}

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\frac{T^{2}}{R^{3}}

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Solution

The correct option is A $\frac{T^{2}}{R^{3}}$
According to $3^{r d}$ law of Kepler
$T^{2} \propto R^{3}$
$\Rightarrow T^{2} = K R^{3}$
where $K$ is a constant
Thus $\frac{T^{2}}{R^{3}}$ does not depends on radius

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Which of the following quantities does not depends upon the orbital radius of the satellite?

The correct option is A T2R3According to 3rd law of KeplerT2∝R3⇒T2=KR3where K is a constantThus T2R3 does not depends on radius

The correct option is A $\frac{T^{2}}{R^{3}}$
According to $3^{r d}$ law of Kepler
$T^{2} \propto R^{3}$
$\Rightarrow T^{2} = K R^{3}$
where $K$ is a constant
Thus $\frac{T^{2}}{R^{3}}$ does not depends on radius