Physics-
General
Easy

Question

A particle crossing the origin of co-ordinates at time t equals 0, moves in the x y-plane with a constant acceleration a in the y-direction. If its equation of motion is y equals b x to the power of 2 end exponent (b is a constant), its velocity component in the x-direction is

  1. square root of fraction numerator 2 b over denominator a end fraction end root  
  2. square root of fraction numerator a over denominator 2 b end fraction end root  
  3. square root of fraction numerator a over denominator b end fraction end root  
  4. square root of fraction numerator b over denominator a end fraction end root  

The correct answer is: square root of fraction numerator a over denominator 2 b end fraction end root


    y equals b x to the power of 2 end exponent
    Differentiating w.r.t. t comma on both sides, we get
    fraction numerator d y over denominator d t end fraction equals b 2 x fraction numerator d x over denominator d t end fraction rightwards double arrow v subscript y end subscript equals 2 b x v subscript x end subscript
    Again, differentiating w.r.t. t comma on both sides, we get
    fraction numerator d v subscript y end subscript over denominator d t end fraction equals 2 b v subscript x end subscript fraction numerator d x over denominator d t end fraction plus 2 b x fraction numerator d v subscript x end subscript over denominator d t end fraction equals 2 b v subscript x end subscript superscript 2 end superscript plus 0
    open square brackets fraction numerator d v subscript x end subscript over denominator d t end fraction close equals 0, because the particle has constant acceleration along y-direction]
    As per question
    fraction numerator d v subscript y end subscript over denominator d t end fraction equals a equals 2 b v subscript x end subscript superscript 2 end superscript semicolon blank v subscript x end subscript superscript 2 end superscript equals fraction numerator a over denominator 2 b end fraction rightwards double arrow v subscript x end subscript equals square root of fraction numerator a over denominator 2 b end fraction end root

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