AP EAMCET · PHYSICS · Gravitation
An artificial satellite is revolving around a planet of radius \(R\) in a circular orbit of radius ' \(a\) '. If the time period of revolution of the satellite, \(T \propto a^{3 / 2} g^x R^y\), then the values of \(x\) and \(y\) are respectively
[ g - acceleration due to gravity]
- A \(1, \frac{1}{2}\)
- B \(\frac{1}{2}, 1\)
- C \(-\frac{1}{2}, \frac{1}{2}\)
- D \(\frac{-1}{2},-1\)
Answer & Solution
Correct Answer
(D) \(\frac{-1}{2},-1\)
Step-by-step Solution
Detailed explanation
\( [T] = [L]^{3/2} ([LT^{-2}])^x ([L])^y \) \( [T] = [L]^{3/2 + x + y} [T]^{-2x} \) \( 1 = -2x \implies x = -1/2 \) \( 0 = 3/2 + x + y \) \( 0 = 3/2 - 1/2 + y \implies y = -1 \)
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