Question

A body weighs 500 gf in air and 450 gf when wholly immersed in water. Calculate
(i) The loss in weight of the body in water.
(ii) The upthrust of the body
(iii) Volume of the body

Answer 1

Hint:The buoyant force or upward force, which an object is immersed partially and wholly in a fluid experience, is known as upthrust. Due to the upthrust, an object immersed partially and wholly in a fluid appears to be lighter. Upthrust mainly depends on two things that are the density and volume of an object immersed.

Complete step by step answer:
Given:
Weight of the body in air W=500 gf.
Weight of the body in water w=450 gf.
We will now express the relation for loss of weight in the body:
$F = W - w$
Here F is the loss of weight in the body.
$ \Rightarrow F = 500\;{\rm{gf - 450}}\;{\rm{gf}}$
$ \Rightarrow F = {\rm{50}}\;{\rm{gf}}$
Thus, the loss in weight of the body is 50 gf.
Since the upthrust in the body is equal to loss in weight of the body, therefore, the upthrust in the body is 50 gf.
Express the formula for upthrust of the body.
${F_T} = Vg\rho $
Here FT is the upthrust, V is the volume occupied by the body, g is the acceleration due to gravity and $\rho $ is the density.
We will now substitute FT=50 gf, $\rho = 1\;{\rm{gc}}{{\rm{m}}^{{\rm{ - 3}}}}$ which is the density of water and g is the acceleration due to gravity.
$\begin{array}{l}
\left( {50\;{\rm{gf}} \times g} \right)\;{\rm{N}} = V \times \;1\;{\rm{gc}}{{\rm{m}}^{{\rm{ - 3}}}} \times g\\
V = 50\;{\rm{c}}{{\rm{m}}^{\rm{3}}}
\end{array}$

Note:For proper clearance of Buoyancy, it's better to understand the concept of density and relative density. The density of the material is mass per unit volume. Specifically, it is the measure of how tightly packed inside a material. Still, a relative density of a substance (also known as specific gravity of substance) is the ratio of its density to water density. If the relative density of a substance is less than one, it will float in water, and if the density of substance is greater than one, it will sink in water.