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Motion in A Plane

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

  • square root of GM over straight R end root
  • square root of 2 square root of 2 GM over straight R end root
  • square root of GM over straight R left parenthesis 1 plus 2 square root of 2 right parenthesis end root
  • 1 half square root of GM over straight R left parenthesis 1 plus 2 square root of 2 right parenthesis end root

D.

1 half square root of GM over straight R left parenthesis 1 plus 2 square root of 2 right parenthesis end root

Net force acting on any one particle M,
 =fraction numerator GM squared over denominator left parenthesis 2 straight R right parenthesis squared end fraction space plus space fraction numerator GM squared over denominator left parenthesis straight R square root of 2 right parenthesis squared end fraction cos space 45 to the power of straight o space plus space fraction numerator GM squared over denominator left parenthesis straight R square root of 2 right parenthesis squared end fraction Cos space 45 to the power of straight o
space equals space GM squared over straight R squared open parentheses 1 fourth plus fraction numerator 1 over denominator square root of 2 end fraction close parentheses


This force will equal to centripetal force
So, Mv squared over straight R space equals space GM squared over straight R squared open parentheses 1 fourth plus fraction numerator 1 over denominator square root of 2 end fraction close parentheses
straight v space equals space square root of fraction numerator GM over denominator 4 straight R end fraction left parenthesis 1 plus 2 square root of 2 right parenthesis end root space equals space 1 half square root of GM over straight R left parenthesis 2 square root of 2 plus 1 right parenthesis end root

Net force acting on any one particle M,
 =fraction numerator GM squared over denominator left parenthesis 2 straight R right parenthesis squared end fraction space plus space fraction numerator GM squared over denominator left parenthesis straight R square root of 2 right parenthesis squared end fraction cos space 45 to the power of straight o space plus space fraction numerator GM squared over denominator left parenthesis straight R square root of 2 right parenthesis squared end fraction Cos space 45 to the power of straight o
space equals space GM squared over straight R squared open parentheses 1 fourth plus fraction numerator 1 over denominator square root of 2 end fraction close parentheses


This force will equal to centripetal force
So, Mv squared over straight R space equals space GM squared over straight R squared open parentheses 1 fourth plus fraction numerator 1 over denominator square root of 2 end fraction close parentheses
straight v space equals space square root of fraction numerator GM over denominator 4 straight R end fraction left parenthesis 1 plus 2 square root of 2 right parenthesis end root space equals space 1 half square root of GM over straight R left parenthesis 2 square root of 2 plus 1 right parenthesis end root

658 Views

What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
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Give three examples of vector quantities.

Force, impulse and momentum.
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What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
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What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors. 


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Give three examples of scalar quantities.

Mass, temperature and energy
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