Given below are two statements:Statement I: A | vedclass

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(B) The time period of a satellite orbiting close to the Earth's surface is given by $T = 2\pi\sqrt{\frac{R_e^3}{GM}}$.Since the mass of the Earth $M

Vedclass · Accepted Answer

Both Statement $I$ and Statement $II$ are true

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(B) The time period of a satellite orbiting close to the Earth's surface is given by $T = 2\pi\sqrt{\frac{R_e^3}{GM}}$.Since the mass of the Earth $M = \rho \cdot \frac{4}{3}\pi R_e^3$,where $\rho$ is the density of the Earth,we can substitute $M$ into the formula:$T = 2\pi\sqrt{\frac{R_e^3}{G(\rho \cdot \frac{4}{3}\pi R_e^3)}} = 2\pi\sqrt{\frac{3}{4\pi G\rho}}$.This shows that $T$ depends on the density $\rho$ of the Earth. Thus,Statement $I$ is true.For a satellite very close to the surface,the gravitational force provides the centripetal force,leading to $g = \frac{GM}{R_e^2}$.Substituting $GM = gR_e^2$ into the general time period formula $T = 2\pi\sqrt{\frac{R_e^3}{GM}}$,we get $T = 2\pi\sqrt{\frac{R_e^3}{gR_e^2}} = 2\pi\sqrt{\frac{R_e}{g}}$.Thus,Statement $II$ is true.

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