The height to which a cylindrical vessel be filled with a homogeneous liquid, to make the average force with which the liquid presses the side of the vessel equal to the force exerted by the liquid on the bottom of the vessel, is equal to
Medium
Download our app for free and get started
(b) Pressure at the bottom = $h\rho g$
and pressure on the vertical surface = $\frac{1}{2}h\rho g$
Now, according to problem
Force at the bottom = Force on the vertical surface
==> $h\rho g \times \pi {r^2} = \frac{1}{2}h\rho g \times 2\pi rh$ $ ==> h = r$
and pressure on the vertical surface = $\frac{1}{2}h\rho g$
Now, according to problem
Force at the bottom = Force on the vertical surface
==> $h\rho g \times \pi {r^2} = \frac{1}{2}h\rho g \times 2\pi rh$ $ ==> h = r$
Download our appand 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
- 1A cubical block is floating in a liquid with one fourth of its volume immersed in the liquid. If whole of the system accelerates upward with acceleration $g / 4$, the fraction of volume immersed in the liquid will be ..........View Solution
- 2View SolutionA boy carries a fish in one hand and a bucket(not full) of water in the other hand . If he places the fish in the bucket , the weight now carried by him (assume that water does not spill) :
- 3A cube of external dimension $10\ cm$ has an inner cubical portion of side $5\ cm$ whose density is twice that of the outer portion. If this cube is just floating in a liquid of density $2\ g/cm^3$, find the density of the inner portionView Solution
- 4A pressure-pump has a horizontal tube of cross-sectional area $10\,cm ^{2}$ for the outflow of water at a speed of $20\,m / s$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is $...N$ [given : density of water $=1000\,kg / m ^{3}$ ]View Solution
- 5An $L-$ shaped glass tube is just immersed in flowing water towards tube as shown. If speed of water current is $V,$ then the height $h$ upto which water rises will beView Solution
- 6View SolutionA wooden piece floats half submerged in a tub of water. If the system is transferred to a lift ascending with acceleration the wooden piece will
- 7The fraction of a floating object of volume ${V_0}$ and density ${d_0}$ above the surface of a liquid of density $d$ will beView Solution
- 8Assume 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 ratioView Solution
- 9What is the velocity $v$ of a metallic ball of radius $r$ falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body ? (The densities of metal and of liquid are $\rho$ and $\sigma$ respectively, and the viscosity of the liquid is $\eta$).View Solution
- 10A cubical block of wood of edge $10$ $cm$ and mass $0.92$ $kg$ floats on a tank of water with oil of rel. density $0.6$ to a depth of $4$ $cm$ above water. When the block attains equilibrium with four of its sides edges verticalView Solution