A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity <math> <mfrac> <mrow> <mrow> <mn>3</mn> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">G</mi> <mi mathvariant="normal">d</mi> </mrow> </mrow> </mfrac> </math> represents:

Time period of satellite T = 2 π R 3 G M <!- [endif]-><!- [endif]-> = 2 π R 3 G d 4 3 π R 3 <!- [endif]-><!- [endif]-> ⇒ T = 3 π G d <!- [endif]-><!- [endif]-> ⇒ 3 π G d = T 2

A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity <math> <mfrac> <mrow> <mrow> <mn>3</mn> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">G</mi> <mi mathvariant="normal">d</mi> </mrow> </mrow> </mfrac> </math> &nbsp;represents: &lt;!-- [if !supportLineBreakNewLine]--&gt; &lt;!--[endif]--&gt;

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Overview Physics Gravitation Physics Class 11th

A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity $\frac{3 π}{G d}$ represents:

Option 1 -

$\sqrt[]{T}$

Option 2 -

Option 3 -

$T^{2}$

Option 4 -

$T^{3}$

2 Views | Posted 3 weeks ago

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1 Answer

Answered by

Raj Pandey | Contributor-Level 9

3 weeks ago

Correct Option - 3

Detailed Solution:

Time period of satellite

$T = 2 π \sqrt[]{\frac{R^{3}}{G M}}$

$= 2 π \sqrt[]{\frac{R^{3}}{G d \frac{4}{3} π R^{3}}}$

$\Rightarrow T = \sqrt[]{\frac{3 π}{G d}}$ $\Rightarrow \frac{3 π}{G d} = T^{2}$

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A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity $\frac{3 π}{G d}$ represents:

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A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity 3 π G d represents:

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A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity $\frac{3 π}{G d}$ represents: