Question

Assertion :For a satellite revolving very near to the earth's surface the time period of revolution is given by $1$h $24$min. Reason: The period of revolution of a satellite depends only upon its height above the earth's surface.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect and Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

We know orbital velocity of a satellite around a planet of mass $M$ having radius of orbit $(r>R)$

$V_0=\sqrt{\frac{GM}{r}}$

Time period $=\frac{2\pi r}{V}=\frac{2\pi r\sqrt{r}}{\sqrt{GM}}=2\pi \sqrt{\frac{R^3}{GM}}$

here $G$ and $M$ are constant

$|Rightarrow Time period depends only on radius (height above earth)

$\therefore$ Time perois for satellite near earth surface

$=2\pi \sqrt{\frac{R}{g}}=\frac{2\pi }{sqrt{\pi }^2}\times \sqrt{6400\times 1000}[\because g\approx {\pi }^2]=2\times 800\times \sqrt{1}0seconds=\frac{2\times 800}{60}\times \sqrt{1}0min=84min=1hr+24min$