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General
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Question

In the arrangement shown in figure the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed

  1. 2 U cos invisible function application theta    
  2. U cos invisible function application theta    
  3. fraction numerator 2 U over denominator cos invisible function application theta end fraction    
  4. fraction numerator U over denominator cos invisible function application theta end fraction    

The correct answer is: fraction numerator U over denominator cos invisible function application theta end fraction



    As P and Q fall down, the length l decreases at the rate of U m/s.
    From the figure, l to the power of 2 end exponent equals b to the power of 2 end exponent plus y to the power of 2 end exponent
    Differentiating with respect to time
    open parentheses text As  end text fraction numerator d b over denominator d t end fraction equals 0 comma fraction numerator d l over denominator d t end fraction equals U close parentheses
    Þfraction numerator d y over denominator d t end fraction equals open parentheses fraction numerator l over denominator y end fraction close parentheses cross times fraction numerator d l over denominator d t end fraction rightwards double arrow fraction numerator d y over denominator d t end fraction equals open parentheses fraction numerator 1 over denominator cos invisible function application theta end fraction close parentheses cross times U equals fraction numerator U over denominator cos invisible function application theta end fraction

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