Physics-
General
Easy

Question

A cube of mass m and density D is suspended from the point P by a spring of stiffness k. The system is kept inside a beaker filled with a liquid of density d. The elongation in the spring, assuming D > d, is:

  1. fraction numerator m g over denominator k end fraction open parentheses 1 minus fraction numerator d over denominator D end fraction close parentheses    
  2. fraction numerator m g over denominator k end fraction open parentheses 1 minus fraction numerator D over denominator d end fraction close parentheses    
  3. fraction numerator m g over denominator k end fraction open parentheses 1 plus fraction numerator d over denominator D end fraction close parentheses    
  4. None of these.    

The correct answer is: fraction numerator m g over denominator k end fraction open parentheses 1 minus fraction numerator d over denominator D end fraction close parentheses


    The cube is in equilibrium under the following three forces,
    V = volume of the immersed portion of the cube. For complete immersion, V = volume of the cube.
    For equilibrium of the cube,kx + Fb = mg
    Þ x = fraction numerator m g minus F subscript b end subscript over denominator k end fraction equals fraction numerator m g minus V d g over denominator k end fraction Where V = (m/D)

    Þ x = fraction numerator m g over denominator k end fraction open parentheses 1 minus fraction numerator d over denominator D end fraction close parentheses

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