WBJEE · Physics · Gravitation
An earth's satellite nejar the surface of the earth takes about 90 min per revolution. A satellite orbiting the moon also takes about 90 min per revolution. Then which of the following is true?
- A \(\rho_m < \rho_e\)
- B \(\rho_m > \rho_e\)
- C \(\rho_{\mathrm{m}}=\rho_{\mathrm{e}}\)
- D No conclusion can be made about the densities
Answer & Solution
Correct Answer
(C) \(\rho_{\mathrm{m}}=\rho_{\mathrm{e}}\)
Step-by-step Solution
Detailed explanation
Hint : \(m\left(E_g\right)=m \omega^2 R\) \(\begin{aligned} & m \cdot 4 \pi \frac{G \rho R}{3}=m \omega^2 R \\ & \Rightarrow \omega^2 \propto \rho \\ & \Rightarrow T \propto \frac{1}{\sqrt{\rho}} \end{aligned}\) If \(\mathrm{T}\) are equal, so will be \(\rho\)
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