Home
Class 11
PHYSICS
If the pressure at half the depth of a t...

If the pressure at half the depth of a tank is equal to `2/3` the pressure at the bottom of the tank, then the height of the water column in the tank is
`("Atmospheric pressure "=10^5N//m^2`)

A

10m

B

15m

C

20m

D

25m

Text Solution

Verified by Experts

The correct Answer is:
C
Let h be the height of the water column and H be the atmospheric pressure.
Then the pressure at the bottom=`H+rhogh`
and the pressure at a depth`h/2` is H+`rhog((h)/(2))`
`:'" "H+rhog((h)/(2))=2/3(H-rhogh)`
`:." "H+rhog((h)/(2))=2/3H+2/3rhogh`
`:." "1/3H=rhogh(2/3-1/2)=1/6rhogh`
`:." "h=(2H)/(rhog)=(2xx10^5)/(10^3xx10)=20m`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • FRICTIONAL IN SOLIDS AND LIQUIDS

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|10 Videos

  • FORCE, WORK AND TORQUE

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|10 Videos

  • MAGNETIC EFFECT OF ELECTRIC CURRENT

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|10 Videos

Similar Questions

Explore conceptually related problems

If pressure at the half depth of a lake is equal to 3/4 times the pressure at its bottom, then find the depth of the lake. [Take g = 10 m/ s^(2) ]

The pressure at the bottom of a tank of liquid is not proprtional to

Knowledge Check

  • If pressure at half the depth of a lake is equal to 2//3 pressure at the bottom of the lake then what is the depth of the lake ?

    A
    10 m
    B
    20 m
    C
    60 m
    D
    30 m

  • The pressure at the bottom of a liquid tank does not depend on :

    A
    Acceleration due to gravity
    B
    density of the liquid
    C
    height of the liquid
    D
    area of the liquid surface

  • The pressure at the bottom of a tank containing a liquid does not depend on

    A
    Acceleration due to gravity
    B
    Height of the liquid column
    C
    Area of the bottom surface
    D
    Nature of the liquid

    • Similar Questions

    Explore conceptually related problems

    The pressure at the bottom of a tank containing a liquid does not depends on

    If the pressure at half of the lake is equal to 1/3 pressure at the bottom of the lake, what is the depth of the take? ("assume" g=10m//s^(2), atm=1xx10^(5) and rho=10^(3)kgm^(-3))

    The level of water in a tank is 5 m high . A hole of the area 10 cm^2 is made in the bottom of the tank . The rate of leakage of water from the hole is

    A liquid of density 800kg m^(-3) is filled in a tank open at the top. The pressure, of the liquid, at the bottom of the tank is 6.4 atmospheres. The velocity of efflux throught a hole at the bottom is ( 1atmosphere = 10^(5)Nm^(-2) )

    There is a hole in the bottom of tank having water. If total pressure at bottom of the tank is 3 atm (1 atm = 10^5 Nm^(-2)) then the velocity of water flowing from the hole is

    Home
    Profile