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Motion In A Plane

Question
CBSEENPH11020250
Wired Faculty App

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

Solution

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

Some More Questions From Motion in A Plane Chapter

What is a scalar quantity?

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

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