the volume of the hollow portion of a sphere is 3/4 of the external volume of the sphere. If it floats in a liquid of relative density /2, half of its external volume immersed, then calculate relative density of the material of the solid?

Asked by Paresh | 11th Dec, 2015, 06:16: PM

Expert Answer:

begin mathsize 14px style Volume space of space hollow space portion space of space the space sphere space is space 3 over 4 space volume space of space the space entire space sphere space left parenthesis straight V right parenthesis. Therefore comma space the space volume space of space the space solid space part space of space the space sphere space is space 1 fourth straight V. Volume space of space the space liquid space displaced space is space equal space to space the space volume space of space sphere space displaced equals straight V over 2. Relative space density space of space liquid space is space 3 over 2. Therefore comma space we space have straight V over 4 cross times left parenthesis straight R. straight D right parenthesis subscript solid cross times straight g equals straight V over 2 left parenthesis straight R. straight D right parenthesis subscript liquid cross times straight g therefore fraction numerator left parenthesis straight R. straight D right parenthesis solid over denominator 4 end fraction equals fraction numerator left parenthesis straight R. straight D right parenthesis liquid over denominator 2 end fraction therefore left parenthesis straight R. straight D right parenthesis subscript solid equals fraction numerator 4 cross times 3 over denominator 2 cross times 2 end fraction equals 3 end style

Answered by Romal Bhansali | 13th Dec, 2015, 01:43: PM