Home
Class 11
PHYSICS
Water pours out rate of Q from a tap, in...

Water pours out rate of Q from a tap, into a cylindrical vessel of radius r. The rate at which the height of water level rises the height is h, is

A

`Q/(pirh)`

B

`Q/(pir^(2))`

C

`Q/(2pir^(2))`

D

`Q/(pir^(2)h)`

Text Solution

Verified by Experts

The correct Answer is:
B

`:.` Volume: `V=pir^(2)h :. (dV)/(dt)=pir^(2)(dh)/(dt)` But `(dV)/(dt)=Q` so `(dh)/(dt)=Q/(pir^(2))`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS

    ALLEN |Exercise Part -II Example|61 Videos

  • MISCELLANEOUS

    ALLEN |Exercise Part -II Example Some worked out Examples|1 Videos

  • KINEMATICS (MOTION ALONG A STRAIGHT LINE AND MOTION IN A PLANE)

    ALLEN |Exercise BEGINNER S BOX-7|8 Videos

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN |Exercise EXERCISE-IV|7 Videos

Similar Questions

Explore conceptually related problems

Coffee is coming out from a conical filter, with height and diameter both are 15 cm into a cylindrical coffee pot with a diameter 15 cm. The rate at which coffee comes out from the filter into the pot is 100 cu cm/min. The rate (in cm/min) at which the level in the pot is rising at the instance when the coffe in the pot is 10 cm, is

A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is tan^(-1)(0.5) . Water is poured into it at a constant rate of 5 cubic meter per hour. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 4 m.

Height of a tank in the form of an inverted cone is 10 m and radius of its circular base is 2 m. The tank contains water and it is leaking through a hole at its vertex at the rate of 0.02m^(3)//s. Find the rate at which the water level changes and the rate at which the radius of water surface changes when height of water level is 5 m.

Water rises to a height h in a capillary at the surface of earth. On the surface of the moon the height of water column in the same capillary will be-

Sand is pouring from a pipe at the rate of 12 cm^(3)//s . The falling sand forms a cone on the ground in such a way that the height of the cone is always one - sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm ?

Water is flowing at the speed of 2.52 km/h through a cylindrical pipe into a cylindrical tank with base radius 40 cm. If the increase in the level of water in the tank in half an hour is 3.15 m, find the internal diameter of the pipe.

Water is drained from a vertical cylindrical tank by opening a valve at the base of the tank. It is known that the rate at which the water level drops is proportional to the square root of water depth y , where the constant of proportionality k >0 depends on the acceleration due to gravity and the geometry of the hole. If t is measured in minutes and k=1/(15), then the time to drain the tank if the water is 4 m deep to start with is (a) 30 min (b) 45 min (c) 60 min (d) 80 min

Spherical marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm,which contains some water. Find the number marbles that should be dropped in to the beaker , so that water level rises by 5.6 cm.

The height to which water rises in a capillary will be

A wooden cylinder of diameter 4 r, height H and density rho//3 is kept on a hole of diameter 2 r of a tank, filled with water of density rho as shown in the If height h_(2) of water level is further decreased, then