A container is containing mercury and water. A uniform solid object stays at equilibrium at the interface between mercury and water such that $$20$$% of the volume of object is in mercury. Find the density (gcc$$−$$1$$ $$) of the object. [Density of mercury is $$13.6$$ gcc−$$1$$, density of water is $$1$$ gcc−$$1$$]

Question

A container is containing mercury and water. A uniform solid object stays at equilibrium at the interface between mercury and water such that $$20$$% of the volume of object is in mercury. Find the density (gcc$$−$$1$$ $$) of the object. [Density of mercury is $$13.6$$ gcc−$$1$$, density of water is $$1$$ gcc−$$1$$]

Infinity Learn · Accepted Answer

At equilibrium,  $$mg=B1+B2$$⇒ρ$$V1+V2g=$$ρ$$1V1g+$$ρ$$2V2g$$⇒ρ$$=$$ρ$$1V1+$$ρ$$2V2V1+V2$$⇒ρ$$=$$  $$13.6$$×$$0.2+1$$×$$0.81=$$  $$3.52$$  g cc−$$1$$

Pressure in a fluid-mechanical properties of fluids

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$A t e q u i l i b r i u m, m g = B_{1} + B_{2}$
$\Rightarrow ρ (V_{1} + V_{2}) g = ρ_{1} V_{1} g + ρ_{2} V_{2} g$
$\Rightarrow ρ = \frac{ρ_{1} V_{1} + ρ_{2} V_{2}}{V_{1} + V_{2}}$
$\Rightarrow ρ = \frac{13.6 \times 0.2 + 1 \times 0.8}{1} = 3.52 g c c^{- 1}$

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Pressure in a fluid-mechanical properties of fluids

Remember concepts with our Masterclasses.

A container is containing mercury and water. A uniform solid object stays at equilibrium at the interface between mercury and water such that 20% of the volume of object is in mercury. Find the density (gcc−1 ) of the object. [Density of mercury is 13.6 gcc−1, density of water is 1 gcc−1]

At equilibrium, mg=B1+B2⇒ρV1+V2g=ρ1V1g+ρ2V2g⇒ρ=ρ1V1+ρ2V2V1+V2⇒ρ= 13.6×0.2+1×0.81= 3.52 g cc−1

Ready to Test Your Skills?

free study material

$A t e q u i l i b r i u m, m g = B_{1} + B_{2}$
$\Rightarrow ρ (V_{1} + V_{2}) g = ρ_{1} V_{1} g + ρ_{2} V_{2} g$
$\Rightarrow ρ = \frac{ρ_{1} V_{1} + ρ_{2} V_{2}}{V_{1} + V_{2}}$
$\Rightarrow ρ = \frac{13.6 \times 0.2 + 1 \times 0.8}{1} = 3.52 g c c^{- 1}$