Question

A rectangular tank is filled to the brim with water. When a hole at its bottom is unplugged, the tank is emptied in time T. If the tank is half-filled with water, it will be emptied in time

Solution

Correct option is

 

The velocity of efflux through a hole is given by 

          

Where h is the height of the tank. If the hole is at the top of the tank, v is obviously zero. Therefore, the average velocity of efflux . If the volume of water in the tank, when it is full, is V and A the cross-sectional area of the hole, then time taken by the tank to be emptied is 

          

When the tank is half-full, V is replaced by  and h is replaced by . Therefore, time taken now is  

        

             .

SIMILAR QUESTIONS

Q1

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

Q2

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.

Q3

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?    

Q4

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 

Q5

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     

Q6

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?

Q7

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 

Q8

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

Q9

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?

Q10

Two capillary tubes A and B of radii ra and rb and lengths la and lbrespectively are held horizontally. The volume of water flowing per second through tube A is Qa when the pressure difference across its ends is maintained at P. When the same pressure difference is maintained across tube B, the volume of water flowing per second through it is Qb. The ratio  is