Question

A body of volume 100 $c{m}^3$ weighs 5 kgf in air. It is completely immersed in a liquid of density 1.8 $\times {10}^{3}kg{m}^{-3}$. 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).

Answer 1

Given: Weight of the body in air, W = 5kgf = 50 N

Volume of the body, V =100 $c{m}^3$ = $100\times {10}^{-6}{m}^3={10}^{-4}{m}^3$

Density of the liquid, d = 1.8 $\times$ 10³ kg/m³

(i) The upthrust due to liquid = dVg
=1.8$\times$10³$\times$10⁻⁴$\times$10
=1.8 N

(ii) The weight of the body in liquid = W-B

= 5 N - 1.8 N
= 3.2 N

(iii) Upthrust on body = Upthrust due to liquid = 1.8 N

The assumption made in part (i) was that the volume of water displaced = volume of the body