A solid sphere falls with a terminal velocity of $$20m/s$$ in air. When another sphere of same radius but made of different material is allowed to fall in air, Its terminal velocity is found to be $$15m/s$$. If density of first sphere is $$2gm/cm3$$ and density of air is $$1.2$$ $$kg/m3$$, find the density of the other sphere.

Question

A solid sphere falls with a terminal velocity of $$20m/s$$ in air. When another sphere of same radius but made of different material is allowed to fall in air, Its terminal velocity is found to be $$15m/s$$. If density of first sphere is $$2gm/cm3$$ and density of air is $$1.2$$ $$kg/m3$$, find the density of the other sphere.

Infinity Learn · Accepted Answer

Terminal velocity $$v=2r29$$ρ$$-$$σηgWhere ρ $$=$$ density of material of sphere σ $$=$$ density of air, η $$=$$ viscosity of air∴$$v2v1=$$ρ$$2-$$σρ$$1-$$σ⇒$$1520=$$ρ$$2-1.22000-1.2$$⇒ρ$$2=1500.3$$ $$kg/m3$$                                                         ⇒ρ$$2=1.5003$$ $$gm/cm3$$

Viscosity

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Viscosity

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Terminal velocity v=2r29ρ-σηgWhere ρ = density of material of sphere σ = density of air, η = viscosity of air∴v2v1=ρ2-σρ1-σ⇒1520=ρ2-1.22000-1.2⇒ρ2=1500.3 kg/m3 ⇒ρ2=1.5003 gm/cm3

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