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
6 months ago
Correct Option - 3
Detailed Solution:

For circular motion Fnet   = M V 2 R

2 F + F ' = M V 2 R

2 G M M ( 2 R ) 2 + G M M ( 2 R ) 2 = M V 2 R                

G M R [ 1 2 + 1 4 ] = V 2              

V = 1 2 G M R ( 2 2 + 1 )

 

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Physics Gravitation 2025

Physics Gravitation 2025

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