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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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Class 10 Class 12

A particle of mass m is moving along the side of a square of side ‘a’, with a uniform speed v in the x-y plane as shown in the figure:

Which of the following statements is false for the angular momentum → L about the origin?

  • bold L space equals space minus fraction numerator mv over denominator square root of 2 end fraction space straight R space straight k with hat on top comma space when space the space paticle space is space moving space from space straight A space to space straight B
  • straight L space equals space mv space open parentheses fraction numerator straight R over denominator square root of 2 end fraction space plus straight a close parentheses space bold k with bold hat on top comma space when space the space particle space is space moving space from space straight B space to space straight C
  • straight L space equals space mv space open parentheses fraction numerator straight R over denominator square root of 2 end fraction space minus straight a close parentheses space straight k with hat on top comma space when space the space particle space is space moving space from space straight B space to space straight C
  • bold L space equals space minus fraction numerator mv over denominator square root of 2 end fraction space straight R space straight k with hat on top comma space when space the space paticle space is space moving space from space straight D space to space straight A

B.

straight L space equals space mv space open parentheses fraction numerator straight R over denominator square root of 2 end fraction space plus straight a close parentheses space bold k with bold hat on top comma space when space the space particle space is space moving space from space straight B space to space straight C

For a particle of mass, m is moving along the side of a square a. Such that
Angular momentum L about the origin

equals space straight L space equals space straight r space straight x space straight p space equals space straight r subscript straight p space sin space straight theta space straight n with hat on top space or space straight L space equals space straight r space left parenthesis straight p right parenthesis straight n with hat on top
When space straight a space particle space is space moving space from space straight D space to space straight A
straight L space equals space fraction numerator straight R over denominator square root of 2 end fraction space mv space left parenthesis negative straight k with hat on top right parenthesis
straight A space particle space is space moving space from space straight A space to space straight B
straight L space equals space fraction numerator straight R over denominator square root of 2 end fraction space mv space left parenthesis negative straight k with hat on top right parenthesis
and space it space moves space from space straight C space to space straight D
space straight L space equals space open parentheses fraction numerator straight R over denominator square root of 2 end fraction plus straight a close parentheses mv space left parenthesis straight k with hat on top right parenthesis
For space straight B space to space straight C comma space we space have space
straight L space space equals space open parentheses fraction numerator straight R over denominator square root of 2 end fraction plus straight a close parentheses mv space left parenthesis straight k with hat on top right parenthesis


For a particle of mass, m is moving along the side of a square a. Such that
Angular momentum L about the origin

equals space straight L space equals space straight r space straight x space straight p space equals space straight r subscript straight p space sin space straight theta space straight n with hat on top space or space straight L space equals space straight r space left parenthesis straight p right parenthesis straight n with hat on top
When space straight a space particle space is space moving space from space straight D space to space straight A
straight L space equals space fraction numerator straight R over denominator square root of 2 end fraction space mv space left parenthesis negative straight k with hat on top right parenthesis
straight A space particle space is space moving space from space straight A space to space straight B
straight L space equals space fraction numerator straight R over denominator square root of 2 end fraction space mv space left parenthesis negative straight k with hat on top right parenthesis
and space it space moves space from space straight C space to space straight D
space straight L space equals space open parentheses fraction numerator straight R over denominator square root of 2 end fraction plus straight a close parentheses mv space left parenthesis straight k with hat on top right parenthesis
For space straight B space to space straight C comma space we space have space
straight L space space equals space open parentheses fraction numerator straight R over denominator square root of 2 end fraction plus straight a close parentheses mv space left parenthesis straight k with hat on top right parenthesis


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