Physics
Fluid-Mechanics
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A hemispherical bowl just floats without sinking in a liquid of density 1 times 2 cross times 10 cubed kgm to the power of negative 3 end exponent.
If the outer diameter and density of the howl are 1m and 2 cross times 10 to the power of 4 kgm to the power of negative 3 end exponent respectively, inner diameter of the bowl would be

  1. open parentheses 3 over 50 close parentheses to the power of 1 divided by 3 end exponent
  2. 2 open parentheses 3 over 50 close parentheses to the power of 1 divided by 3 end exponent
  3. open parentheses 47 over 50 close parentheses to the power of 1 divided by 3 end exponent
  4. open parentheses 47 over 50 close parentheses to the power of 1 divided by 3 end exponent

The correct answer is: open parentheses 47 over 50 close parentheses to the power of 1 divided by 3 end exponent


    table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell 2 over 3 pi open parentheses R cubed minus r cubed close parentheses rho subscript s g equals 2 over 3 pi R cubed rho subscript L g end cell row cell open parentheses R cubed minus r cubed close parentheses rho subscript s equals R cubed rho subscript L end cell row cell fraction numerator R cubed minus r cubed over denominator R cubed end fraction equals fraction numerator 1 times 2 over denominator 20 end fraction equals 3 over 50 semicolon r cubed equals 1 minus 3 over 50 equals open parentheses 47 over 50 close parentheses not stretchy rightwards double arrow r equals open parentheses 47 over 50 close parentheses to the power of 1 divided by 3 end exponent end cell end table

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