Mechanical Properties of Fluids

A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball $\left(v\right)$ as a function of time $\left(t\right)$ is

A $U$tube with both ends open to the atmosphere is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of $10\mathrm{mm}$above the water level on the…

A rectangular film of liquid is extended from $(4\mathrm{}\mathrm{cm}\times\,2\mathrm{}\mathrm{cm})$ to $(5\mathrm{}\mathrm{cm}\times\,4\mathrm{}\mathrm{cm})$. If the work done is $3\times\,10^{-4}J$, the value of the…

A certain number of spherical drops of a liquid of radius $r$ coalesce to form a single drop of radius $R$ and volume $V.$ If $T$ is the surface tension of the liquid then:

A wind with speed $40ms^{-1}$ blows parallel to the roof of a house. The area of the roof is $250m^{2}$ . Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof…

A capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$. The mass of the water in the capillary is $5g$. Another capillary tube of radius $2r$ is immersed in water. The mass of water…

A small hole of area cross-section $2mm^{2}$ is present near the bottom of a fully filled open tank of height $2m.$ Taking $g=10ms^{-2}$, the rate of flow of water through the open hole would be nearly

Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is ______ .

Small water droplets of radius $0.01 \mathrm{~mm}$ are formed in the upper atmosphere and falling with a terminal velocity of $10 \mathrm{~cm} / \mathrm{s}$. Due to condensation, if 8 such droplets are coalesced and…

A capillary tube made of glass of radius $0.15mm$is dipped vertically in a beaker filled with methylene iodide (surface tension $=0.05Nm^{-1}$, density$=667kgm^{-3}$) which rises to height$h$in the tube. It is observed…

A thin tube sealed at both ends is $100 \mathrm{~cm}$ long. It lies horizontally, the middle $20 \mathrm{~cm}$ containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now…

Eight mercury drops, each of radius $r$, coalesce to form a bigger drop. The surface energy released in this process is _______. ($S$ is the surface tension of mercury).