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Standard XII

Physics

Speed of Efflux

Water ρ=1000 ...

Question

Water $(ρ = 1000 {kg/m}^{3})$ and kerosene $(ρ = 800 {kg/m}^{3})$ are filled separately in two identical cylindrical vessels having small heights. Both vessels have small holes at their bottom. The speed of the water and kerosene coming out of their holes are $v_{1}$ and $v_{2}$ respectively. Select the correct option.

v_{1} = v_{2}

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v_{1} = 3 v_{2}

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v_{1} = 2 v_{2}

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v_{1} = 4 v_{2}

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Solution

The correct option is A $v_{1} = v_{2}$
Given,
Speed of water $(ρ = 1000 {kg/m}^{3})$ coming out of hole $= v_{1}$
Speed of kerosene $(ρ = 800 {kg/m}^{3})$ coming out of hole $= v_{2}$
We know that for small heights of vessels, speed of efflux is independent of density of fluid.
Speed of efflux for small holes, $v = \sqrt{2 g h}$ which is independent of density.

Therefore, $v_{1} = v_{2}$

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Speed of Efflux

Standard XII Physics

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Water (ρ=1000 kg/m3) and kerosene (ρ=800 kg/m3) are filled separately in two identical cylindrical vessels having small heights. Both vessels have small holes at their bottom. The speed of the water and kerosene coming out of their holes are v1 and v2 respectively. Select the correct option.