If an object is having same weight at same distance above and below the surface of earth, find its distance from surface of earth.

Option 1 -

$\frac{R}{2}$

Option 2 -

$(\sqrt[]{5} - 1) \frac{R}{2}$

Option 3 -

$(\sqrt[]{3} - 1) \frac{R}{2}$

Option 4 -

$(\sqrt[]{5} - 1) R$

2 Views | Posted 3 weeks ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

3 weeks ago

Correct Option - 2

Detailed Solution:

$\frac{G M m}{{(R + x)}^{2}} = \frac{G M m (R - x)}{R^{3}}$

->R³ = (R + x)² (R – x)

->R³ = (R²– x²) (R + x)

->x² + Rx – R² = 0

$x = \frac{- R \pm \sqrt[]{R + 4 R^{2}}}{2}$

$x = \frac{(\sqrt[]{5 R} - 1)}{2} R$

<!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1820654903"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <mfrac> <mrow> <mi>G</mi> <mi>M</mi> <mi>m</mi> </mrow> <mrow> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mi>R</mi> <mo>+</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>G</mi> <mi>M</mi> <mi>m</mi> <mtext> </mtext> <mrow> <mo> (</mo> <mrow> <mi>R</mi> <mo>−</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <mrow> <mi>R</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> ->R3 = (R + x)2 (R – x)->R3 = (R2– x2) (R + x)->x2 + Rx – R2 = 0 <math> <mrow> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mo>−</mo> <mi>R</mi> <mo>±</mo> <mroot> <mrow> <mi>R</mi> <mo>+</mo> <mn>4</mn> <msup> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1820654904"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mo> (</mo> <mrow> <mroot> <mrow> <mn>5</mn> <mi>R</mi> </mrow> <mrow></mrow> </mroot> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>R</mi> </mrow> </math>             <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1820654910"> </o:OLEObject></xml><! [endif]->

0 Upvotes 0 Downvotes

If an object is having same weight at same distance above and below the surface of earth, find its distance from surface of earth.

1 Answer

Similar Questions for you

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question