Question

Two identical cylindrical vessels, each of base area A, have their bases at the same horizontal level. They contain a liquid of density . In one vessel the height of the liquid is h1 and in the other h2 > h1. When the two vessels are connected, the work done by gravity in equalizing the levels is

Solution

Correct option is

 

After the levels in the two vessels becomes equal, the increase in height of the liquid in one vessel is  with the same decrease in height in the other. Thus, effectively a slab of liquid  in thickness falls a vertical distance equal to its thickness under the action of gravity. 

Therefore, 

Work done by the gravity is 

           

Where mass of slab m is given by    

           

Therefore, 

          

               .

SIMILAR QUESTIONS

Q1

The dimensions of viscosity in terms of M, L and T are

Q2

The dimensions of Reynold’s number are

Q3

A rain drop of radius r falls in air with a terminal speed vt. What is the terminal speed of a rain drop of radius 2r

Q4

Eight spherical rain drops of the same mass and radius are falling down a terminal speed of 6 cms–1. If they coalesce to form one big drop, what will be its terminal speed? Neglect the buoyancy due to air.

Q5

Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of water is p at a point where the velocity of flow is v, what is the pressure at another point where the velocity of flow is 2v being the density of water?    

Q6

The cylindrical tube of a spray pump has a radius R, one end of which hasn fine holes, each of radius r. If the speed of flow of the liquid in the tube is V, the speed of ejection of the liquid through the holes is 

Q7

In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the lower and upper surfaces of the wing are v and  respectively. If the density of air is  and the surface area of the wing is A, the dynamic lift on the wing is given by     

Q8

A piece of copper having an internal cavity weights 264 g in air and 221 g in water. The density of copper is 8.8 gm–3. What is the volume of the cavity?

Q9

A stone of relative density k is released from rest on the surface of a lake. If viscous effects are ignored, the stone sinks in water with an acceleration of 

Q10

A cylindrical jar has radius r. To what height h should it be filled with a liquid so that the force exerted by the liquid on the sides of the jar equals the force exerted on the bottom?