Physics
Fluid-Mechanics
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A wooden block of mass m and density d is tied to a string, the other end of the string is fixed to the bottom of a tank. The tank is filled with a liquid of density  sigma text  with  end text sigma greater than d.  What is the tension in the string

  1. open parentheses fraction numerator sigma minus d over denominator sigma end fraction close parentheses m g
  2. open parentheses fraction numerator sigma minus d over denominator d end fraction close parentheses m g
  3. fraction numerator d m g over denominator sigma end fraction
  4. fraction numerator sigma m g over denominator d end fraction

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


    text  Volume of block  end text equals m over d
text  Now upthrust = weight of water displaced  end text equals fraction numerator m sigma g over denominator d end fraction text  .  end text
    This is the upward force on the block due to buoyancy.
    The downward force on the block = its weight = m g
    T equals fraction numerator m sigma g over denominator d end fraction minus m g equals open parentheses fraction numerator sigma minus d over denominator d end fraction close parentheses m g

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