Physics
Fluid-Mechanics
Easy

Question

Two blocks A and B are made of different kinds of wood. Block A floats in with 1 fourth to the power of t h end exponent text  of  end text
its above the surface of water. Block B floats in water with 2 over 3 r d s of volume below the surface of water. The ratio of the densities of A and B is

  1. 3: 2
  2. 5: 3
  3. 9: 8
  4. 4: 3

The correct answer is: 9: 8


    text  Let  end text V subscript 1 text  be the volume of block  end text straight A text  and  end text rho subscript 1 text  is density. Then, from the principle of flotation, we have  end text
rho subscript 1 V subscript 1 g equals open parentheses 1 minus 1 fourth close parentheses V cross times rho cross times g text  or  end text rho subscript 1 equals fraction numerator 3 p over denominator 4 end fraction
text  Where  end text rho text  is the density of water. Similarly for block  end text B text  we have  end text rho subscript 2 V subscript 2 g equals fraction numerator 2 V over denominator 3 end fraction rho g text  or  end text rho subscript 2 equals fraction numerator 2 p over denominator 3 end fraction
therefore rho subscript 1 over rho subscript 2 equals fraction numerator 3 p over denominator 4 end fraction cross times fraction numerator 3 over denominator 2 p end fraction equals 9 over 8

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