First slide

Pressure in a fluid-mechanical properties of fluids

Question

Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is 36 g and its density is 9 g / cm³. If the mass of the other is 48 g, its density in g / cm³ is

Moderate

A

$\frac{4}{3}$
B

$\frac{3}{2}$
C

3
D

5

Solution

Apparent weight $= V (ρ - σ) g = \frac{m}{ρ} (ρ - σ) g$
where m = mass of the body,
$ρ =$ density of the body
$σ =$ density of water
If two bodies are in equilibrium then their apparent weight must be equal.
$\frac{m_{1}}{ρ_{1}} (ρ_{1} - σ) = \frac{m_{2}}{ρ_{2}} (ρ_{2} - σ)$
$\Rightarrow \frac{36}{9} (9 - 1) = \frac{48}{ρ_{2}} (ρ_{2} - 1)$
By solving we get $ρ_{2} = 3$ .

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