A large vessel with a small hole at the bottom is filled with water and kerosene with kerosene floating on water. The length of water column is 20 m and that of kerosene is 25 cm. The velocity with which water flows out of the hole is (density of kerosine = 0.8 gcm-3 neglect viscous force ).

# A large vessel with a small hole at the bottom is filled with water and kerosene with kerosene floating on water. The length of water column is 20 m and that of kerosene is 25 cm. The velocity with which water flows out of the hole is (density of kerosine = 0.8 gcm-3 neglect viscous force ).

1. A

5.6ms-1

2. B

0.7ms-1

3. C

2.8ms-1

4. D

1.4ms-1

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### Solution:

Given,

Length of the water = 20m

length of kerosene = 25cm

From the question,

${\mathrm{\rho }}_{\mathrm{k}}\mathrm{gh}+{\mathrm{\rho }}_{\mathrm{w}}\mathrm{gh}=\frac{1}{2}{\mathrm{\rho }}_{\mathrm{w}}{\mathrm{v}}^{2}$

substituting the value,

${\mathrm{\rho }}_{\mathrm{k}}\mathrm{g}×0.25+{\mathrm{\rho }}_{\mathrm{w}}\mathrm{g}×0.2=\frac{1}{2}{\mathrm{\rho }}_{\mathrm{w}}{\mathrm{v}}^{2}$

$\frac{\left(800×10×0.25+1000×10×0.2\right)×2}{1000}={\mathrm{v}}^{2}$

$\mathrm{v}=\sqrt{0.2\left(0.8×2.5+2\right)}=\sqrt{2\left(2+2\right)}=2.8\mathrm{m}/\mathrm{s}$

Hence the correct answer is 2.8m/s.

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