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A body is projected up a smooth inclined plane with a velocity v subscript 0 end subscript from the point A as shown in figure. The angle of inclination is 45 degree and top B of the plane is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of v subscript 0 end subscript? Length of the inclined plane is 20 square root of 2 m, and g equals 10 m s to the power of negative 2 end exponent

  1. 20 blank m s to the power of negative 1 end exponent    
  2. 20 square root of 2 m s to the power of negative 1 end exponent    
  3. 40 blank m s to the power of negative 1 end exponent    
  4. 40 square root of 2 blank m s to the power of negative 1 end exponent    

The correct answer is: 20 square root of 2 m s to the power of negative 1 end exponent


    Let v be the velocity acquired by the body at B which will be moving making an angle 45 degree with the horizontal direction. As the body just crosses the well so fraction numerator v to the power of 2 end exponent over denominator g end fraction equals 40
    or v to the power of 2 end exponent equals 40 g equals 40 cross times 10 equals 400
    or v equals 20 blank m s to the power of negative 1 end exponent
    Taking motion of the body from A to B along the inclined plane we have
    u equals v subscript 0 end subscript comma a equals negative g sin invisible function application 45 degree equals negative fraction numerator 10 over denominator square root of 2 end fraction m s to the power of negative 2 end exponent
    s equals 20 m comma v equals 20 m s to the power of negative 1 end exponent
    As v to the power of 2 end exponent equals u to the power of 2 end exponent plus 2 a s
    therefore blank 400 equals v subscript 0 end subscript superscript 2 end superscript plus 2 open parentheses negative fraction numerator 10 over denominator square root of 2 end fraction close parentheses cross times 20 square root of 2
    or v subscript 0 end subscript superscript 2 end superscript equals 400 plus 400 equals 800 or v equals 20 square root of 2 m s to the power of negative 1 end exponent

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