A large vessel of height $H$, is filled with a liquid of density $\rho$, upto the brim. A small hole of radius $r$ is made at the side vertical face, close to the base. The horizontal force is required to stop the gushing of liquid is ...........
Easy
Download our app for free and get startedPlay store
(a)

Pressure close to the base $=\rho g H$

Force required $=$ pressure $\times$ area of hole $=\rho g H\left(\pi r^2\right)$

art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    A wind with speed $40\,\, m/s$ blows parallel to the roof of a house. The area of the roof is $250\, m^2.$ Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be  $(\rho _{air} = 1.2  \,\,kg/m^3)$ 
    View Solution
  • 2
    A cylinder of height $h$ is filled with water and is kept on a block of height $h / 2$ . The level of water in the cylinder is kept constant. Four holes numbered $1, 2, 3$ and $4$ are at the side of the cylinder and at heights $0,\ h / 4,\ h / 2$ and $3h / 4$ respectively. When all four holes are opened together, the hole from which water will reach farthest distance on the plane $PQ$ is the hole number
    View Solution
  • 3
    A liquid of density $750\,kgm ^{-3}$ flows smoothly through a horizontal pipe that tapers in crosssectional area from $A _{1}=1.2 \times 10^{-2}\,m ^{2}$ to $A_{2}=\frac{A_{1}}{2}$. The pressure difference between the wide and narrow sections of the pipe is $4500\,Pa$. The rate of flow of liquid is________$\times 10^{-3}\,m ^{3} s ^{-1}$
    View Solution
  • 4
    A cubical block of side $0.5\,m$ floats on water with $30\%$ of its volume under water. ....... $kg$ is the maximum weight that can be put on the block without fully submerging it under water ? [Take density of water $= 10^3\,kg/m^3$ ]
    View Solution
  • 5
    A liquid flows in a tube from left to right as shown in figure. ${A_1}$ and ${A_2}$ are the cross-sections of the portions of the tube as shown. Then the ratio of speeds ${v_1}/{v_2}$ will be
    View Solution
  • 6
    Assume that, the drag force on a football depends only on the density of the air, velocity of the ball and the cross-sectional area of the ball. Balls of different sizes but the same density are dropped in an air column. The terminal velocity reached by balls of masses $250 \,g$ and $125 \,g$ are in the ratio
    View Solution
  • 7
    In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $70 \mathrm{~ms}^{-1}$ and $65 \mathrm{~ms}^{-1}$ respectively. If the wing area is $2 \mathrm{~m}^2$ the lift of the wing is__________ $\mathrm{N}$.

    (Given density of air $=1.2 \mathrm{~kg} \mathrm{~m}^{-3}$ )

    View Solution
  • 8
    $Assertion :$ Falling raindrops acquire a terminal velocity.
    $Reason :$ A constant force in the direction of motion and a velocity dependent force opposite to the direction of motion, always result in the acquisition of terminal velocity.
    View Solution
  • 9
    A cubical block of side $‘a’$ and density $‘\rho ’$ slides over a fixed inclined plane with constant velocity $‘v’$. There is a thin film of viscous fluid of thickness $‘t’$ between the plane and the block. Then the coefficient of viscosity of the thin film will be:
    View Solution
  • 10
    Water from a pipe is coming at a rate of $100\, litres$ per minute. If the radius of the pipe is $5\, cm$, the Reynolds number for the flow is of the order of : (density of water $= 1000\, kg/m^3$, coefficient of viscosity of water $= 1\, mPa\, s$)
    View Solution