Question

Water has 1000 density kerosene has 800 density fill in similar cylinder both vessel have same hole at bottom the speed of water and kerosene v1 and v2 relationship between both velocity

Answer 1

Answer:

Given:

Water and Kerosene of different densities have been filled in similar cylinders. Same holes are present at bottom of cylinder.

To find:

Ratio of Speed of ejection of water through the holes .

Concept:

For any cylinder having a small hole (through which liquid can be ejected) and liquid filled upto height h , we can say that :

$\boxed{ \huge{ \red{ \sf{v = \sqrt{2gh}}}}}$

Diagram:

Please see the attached photo to understand better.

Calculation:

From the relationship , we can easily understand that the Velocity of ejection is not dependent on the density of fluid in the cylinder.

Since both ways and oil had been put in the cylinder upto the same height , we can say that :

$\boxed{ \large{ \red{ \sf{v1 = \sqrt{2gh}.....(water)}}}}$

and

$\boxed{ \large{ \red{ \sf{v2 = \sqrt{2gh}.....(oil)}}}}$

So ratio of v1 and v2 will be :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \huge{ \sf{ \orange{1 \: : \: 1}}}}$

Answer 2

$\underline{ \mathfrak{\huge{\boxed{\fcolorbox{purple}{orange}{\purple{Answer\::-}}}}}} \\ \\ \star \rm \: \red{Given}$

• A different density material water and kerosene fill in similar cylinder
• Both vassel have same hole at bottom

$\star \rm \: \red{To \: Find}$

• ratio of velocity of ejection

$\star \rm \: \red{Formula}$

Velocity of ejection for a material from hole which is at height 'h' is given by...

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \dagger \: \underline{ \boxed{ \bold{ \rm{ \pink{V = \sqrt{2gh}}}}}} \: \dagger$

$\star \rm \: \red{Calculation}$

• let velocity of ejection for water is V1

$\rm \: \leadsto \blue{V_1 = \sqrt{2gh}}$

• let velocity of ejection for kerosene is V2

$\leadsto \rm \: \blue{V_2 = \sqrt{2gh}}$

• Now, take ratio of velocity of ejection

$\dagger \: \underline{ \boxed{ \rm{ \orange{ \bold{V_1 \::\: V_2 = 1 \::\: 1}}}}} \: \dagger$

$\star \rm \: \red{Remember}$

Velocity of ejection from hole does not depend upon density of material...