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Q. A body weighs $50$ grams in air and $40$ grams in water. How much would it weigh in a liquid of specific gravity $1.5$ ?

KCETKCET 2008Mechanical Properties of Fluids

Solution:

$ \frac{\sigma_{L}}{\sigma_{W}} =\frac{\text { upthrust on body in liquid }}{\text { upthrust on body in water }} $
$\frac{1.5}{1} =\frac{x}{[50-40] \,g } $
$\Rightarrow \,\,\,\,\, x=15 \,g$
$\therefore $ upthrust on body in liquid $=15\, g$
Weight of the body $=50 \,g$
Hence, body will weigh $(50-15)=35 \,g$ in the liquid.