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Question

A block [b] is attached to two unstretched springs S subscript 1 end subscript and S subscript 2 end subscript with spring constants k and 4 k, respectively (see figure I). The other ends are attached to identical supports M subscript 1 end subscript and M subscript 2 end subscript not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio fraction numerator y over denominator x end fraction is

  1. 4    
  2. 2    
  3. fraction numerator 1 over denominator 2 end fraction    
  4. fraction numerator 1 over denominator 4 end fraction    

The correct answer is: fraction numerator 1 over denominator 2 end fraction



    As springs and supports (M subscript 1 end subscript and M subscript 2 end subscript) are having negligible mass. Whenever springs pull the massless supports, springs will be in natural length. At maximum compression, velocity of B will be zero

    And by energy conservation
    fraction numerator 1 over denominator 2 end fraction open parentheses 4 K close parentheses y to the power of 2 end exponent equals fraction numerator 1 over denominator 2 end fraction K x to the power of 2 end exponent rightwards double arrow fraction numerator y over denominator x end fraction equals fraction numerator 1 over denominator 2 end fraction

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