How is the upthrust related to the volume of the body submerged in a liquid?

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Solution

Upthrust force acting on a submerged body is equal the weight of the liquid displaced whose volume is equal to volume of the submerged body.

Expression for upthrust force:

$F_{b} = W e i g h t o f l i q u i d d i s p l a c e d b y i m m e r s e d p o r t i o n = (d e n s i t y o f l i q u i d) \times (v o l u m e o f l i q u i d d i s p l a c e d) \times g = (d e n s i t y o f l i q u i d) \times (v o l u m e o f s u b m e r g e d p o r t i o n o f t h e b o d y) \times g$

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How is the upthrust related to the volume of the body submerged in a liquid ?

A body of volume 100 $c m^{3}$ weighs 5 kgf in air. It is completely immersed in a liquid of density 1.8 $\times 10^{3} k g m^{- 3}$ . Find :
(i) the upthrust due to liquid and
(ii) the weight of the body in liquid.
(iii) the upthrust on the body.
State the assumption made in part (i).