Four particle each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is:

Four particle each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is:

Option 1 - <p><span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mroot> <mrow> <mfrac> <mrow> <mi>G</mi> <mi>M</mi> </mrow> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>
Option 2 - <p><span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mroot> <mrow> <mfrac> <mrow> <mi>G</mi> <mi>M</mi> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>
Option 3 - <p><span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mroot> <mrow> <mfrac> <mrow> <mi>G</mi> <mi>M</mi> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>
Option 4 - <p><span contenteditable="false"> <math> <mrow> <mroot> <mrow> <mfrac> <mrow> <mi>G</mi> <mi>M</mi> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>
2 Views|Posted 6 months ago
Asked by Shiksha User
1 Answer
A
Answered by
6 months ago
Correct Option - 3
Detailed Solution:
For circular motion Fnet

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->R3 = (R + x)2 (R – x)
->R3 = (R2– x2) (R + x)
->x2 + Rx – R2 = 0
R is not correct.
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