MHT CET · Physics · Gravitation
The time period \(T\) of a satellite is related to the density \((\rho)\) of the plane which is orbiting close around the planet as.
- A \(T \propto \rho^{1 / 2}\)
- B \(T \propto \rho\)
- C \(T \propto \rho^{-3 / 2}\)
- D \(T \propto \rho^{-1 / 2}\)
Answer & Solution
Correct Answer
(D) \(T \propto \rho^{-1 / 2}\)
Step-by-step Solution
Detailed explanation
According to Kepler's Law of orbits
\(T^2 \propto R^3\)
Density \(\rho \propto \frac{M}{\left(\frac{4}{3} \pi R^3\right)} \Rightarrow \rho \propto R^{-3}\)
\(\Rightarrow T^2 \propto \frac{1}{\rho} \Rightarrow T \propto \rho^{\frac{-1}{2}}\)
\(T^2 \propto R^3\)
Density \(\rho \propto \frac{M}{\left(\frac{4}{3} \pi R^3\right)} \Rightarrow \rho \propto R^{-3}\)
\(\Rightarrow T^2 \propto \frac{1}{\rho} \Rightarrow T \propto \rho^{\frac{-1}{2}}\)
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