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Motion in A Plane

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Physics Part I

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Physics

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Class 10 Class 12

Two particles A and B, move with constant velocities v1 and v2. At the initial moment, their position vectors are r1 and r2 respectively. The condition for particles A and B for their collision is 

  • fraction numerator straight r subscript 1 space equals space straight r subscript 2 over denominator vertical line straight r subscript 1 minus straight r subscript 2 vertical line end fraction space equals space fraction numerator v subscript 2 space equals space v subscript 1 over denominator vertical line v subscript 2 minus v subscript 1 vertical line end fraction
  • r1.v1 = r2.v2

  • r1 x v1 = r2 x v2

  • r1 - r2 = v1-v2


A.

fraction numerator straight r subscript 1 space equals space straight r subscript 2 over denominator vertical line straight r subscript 1 minus straight r subscript 2 vertical line end fraction space equals space fraction numerator v subscript 2 space equals space v subscript 1 over denominator vertical line v subscript 2 minus v subscript 1 vertical line end fraction

For two particles A and B moves with constant velocitites v1 and v2, such that two particles to collide, the direction of the relative velocity of one with respect to other should be directed towards the relative position of the other particle.i.e., fraction numerator straight r subscript 1 minus straight r subscript 2 over denominator vertical line straight r subscript 1 minus straight r subscript 2 vertical line end fraction space rightwards arrow spacedirection of relative position of 1 w.r.t

similarly, fraction numerator straight v subscript 1 minus straight v subscript 2 over denominator vertical line straight v subscript 1 minus straight v subscript 2 vertical line end fraction space rightwards arrow direction of velocity of 2 w.r.t 1
so, for collision of A and B, we get


fraction numerator straight r subscript 1 space equals space straight r subscript 2 over denominator vertical line straight r subscript 1 minus straight r subscript 2 vertical line end fraction space equals space fraction numerator v subscript 2 space equals space v subscript 1 over denominator vertical line v subscript 2 minus v subscript 1 vertical line end fraction

For two particles A and B moves with constant velocitites v1 and v2, such that two particles to collide, the direction of the relative velocity of one with respect to other should be directed towards the relative position of the other particle.i.e., fraction numerator straight r subscript 1 minus straight r subscript 2 over denominator vertical line straight r subscript 1 minus straight r subscript 2 vertical line end fraction space rightwards arrow spacedirection of relative position of 1 w.r.t

similarly, fraction numerator straight v subscript 1 minus straight v subscript 2 over denominator vertical line straight v subscript 1 minus straight v subscript 2 vertical line end fraction space rightwards arrow direction of velocity of 2 w.r.t 1
so, for collision of A and B, we get


fraction numerator straight r subscript 1 space equals space straight r subscript 2 over denominator vertical line straight r subscript 1 minus straight r subscript 2 vertical line end fraction space equals space fraction numerator v subscript 2 space equals space v subscript 1 over denominator vertical line v subscript 2 minus v subscript 1 vertical line end fraction

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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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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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Give three examples of scalar quantities.

Mass, temperature and energy
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