A solid of density $5000 K g / m^{3}$ weight $(0.5 K g) \times g$ in air. It is completely immersed in water of density $1000 K g / m^{3}$ . Calculate the apparent weight of the solid in water.

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Solution

Step1: Given data
The density of the solid is $ρ_{s} = 5000 K g / m^{3} .$
The weight of the solid is $W_{s} = (0.5 K g) \times g$
The density of water is $ρ_{w} = 1000 K g / m^{3}$
Step2: The apparent weight of a body in a solid
Volume is the ratio of mass and density, i.e, $V = \frac{m}{ρ}$ , where, m is the mass of the body and $ρ$ is the density of the body.
We know the apparent weight of a body in a liquid is, $W_{a} = A c t u a l w e i g h t o f t h e b o d y - b u o y a n c y f o r c e o n t h e b o d y$ .
The buoyancy force exerted on a body in a liquid is equal to the weight of the displaced water due to the body. Buoyancy is defined by the form, $F_{b} = (V \times ρ_{w}) g$ , where, V is the volume of the body and $ρ_{w}$ is the density of the liquid, and g is the acceleration due to gravity.
Step3: Diagram
Step4: Finding the buoyancy force
The volume of the solid is
$V = \frac{m}{ρ} = \frac{0.5}{5000} = 10000 o r V = 10^{- 4} m^{3} . . . . . . . . . . . . . . . . (1)$
The buoyancy force exerted on the body when it is in the water is
$F_{b} = (V \times ρ_{w}) g = (10^{- 4}) \times (1000 K g) g o r F_{b} = (0.1 K g) g . . . . . . . . . . . . . (2)$
Step5: Finding the apparent weight
As we know, $W_{a} = A c t u a l w e i g h t o f t h e b o d y - b u o y a n c y f o r c e o n t h e b o d y$
From equations 1 and 2 we get,
The apparent weight of the body is
$W_{a} = (0.5 K g) g - (0.1 K g) g o r W_{a} = (0.4 K g) g$
Therefore, the apparent weight of the solid in water $(0.4 K g) g$ .

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A solid of density 5000Kg/m3 weight 0.5Kg×g in air. It is completely immersed in water of density 1000Kg/m3. Calculate the apparent weight of the solid in water.

A solid of density $5000 K g / m^{3}$ weight $(0.5 K g) \times g$ in air. It is completely immersed in water of density $1000 K g / m^{3}$ . Calculate the apparent weight of the solid in water.