A satellite is orbiting just above the surface of the earth with period T. If <math> <mi>d</mi> </math> is the density of the earth and <math> <mi>G</mi> </math> 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:

B ? P = B ? upper wire ⊗ + B ? semi-circle ? + B ? lower-wire ⊗ B P = - μ 0 i 4 π R + μ 0 i 4 R - μ 0 i 4 π R = μ 0 i 4 R 1 - 2 π pointing away from the page

A satellite is orbiting just above the surface of the earth with period T. If <math> <mi>d</mi> </math> is the density of the earth and <math> <mi>G</mi> </math> 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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Physics NCERT Exemplar Solutions Class 11th Chapter Eight 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 -

$T$

Option 3 -

$T^{2}$

Option 4 -

$T^{3}$

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 4

Detailed Solution:

${\overset{?}{B}}_{P} = {\overset{?}{B}}_{upper wire} \otimes + {\overset{?}{B}}_{semi-circle} ? + {\overset{?}{B}}_{lower-wire} \otimes$

$B_{P} = - \frac{μ_{0} i}{4 π R} + \frac{μ_{0} i}{4 R} - \frac{μ_{0} i}{4 π R}$ $= \frac{μ_{0} i}{4 R} (1 - \frac{2}{π})$ pointing away from the page

<math> <msub> <mrow> <mrow> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">P</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mrow> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> </mrow> </mrow> <mrow> <mrow> <mtext>upper wire</mtext> <mtext> </mtext> </mrow> </mrow> </msub> <mo>⊗</mo> <mo>+</mo> <msub> <mrow> <mrow> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> </mrow> </mrow> <mrow> <mrow> <mtext>semi-circle</mtext> <mtext> </mtext> </mrow> </mrow> </msub> <mo>? </mo> <mo>+</mo> <msub> <mrow> <mrow> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> </mrow> </mrow> <mrow> <mrow> <mtext>lower-wire</mtext> <mtext> </mtext> </mrow> </mrow> </msub> <mo>⊗</mo> </math> <math> <msub> <mrow> <mrow> <mi>B</mi> </mrow> </mrow> <mrow> <mrow> <mi>P</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mi>i</mi> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> <mi>π</mi> <mi>R</mi> </mrow> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mi>i</mi> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> <mi>R</mi> </mrow> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mi>i</mi> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> <mi>π</mi> <mi>R</mi> </mrow> </mrow> </mfrac> </math> <math> <mo>=</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mi mathvariant="normal">i</mi> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> <mi mathvariant="normal">R</mi> </mrow> </mrow> </mfrac> <mfenced separators="|"> <mrow> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </math> pointing away from the page

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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: