Mechanical properties of fluids practice · Mixed difficulty

The wettability of a surface by a liquid depends primarily on

Suppose that 64 raindrops combine into a single drop. Calculate the ratio of the total surface energy of the 64 drops to that of a single drop.

Where $\mathrm{T}=0.072 \mathrm{~N} / \mathrm{m}$

A raft of wood of density $600 \mathrm{~kgm}^{-3}$ and mass $120 \mathrm{~kg}$ floats in water. How much weight (in $\mathrm{kg}$ ) can be put on the raft to make it just sink?

The reading of pressure meter attached with a closed pipe is $3.5 \times 10^4 \mathrm{~N} / \mathrm{m}^2$. On opening the valve of the pipe, the reading of the pressure meter is reduced to $3.0 \times 10^5$ $\mathrm{N} / \mathrm{m}^2$. Calculate the speed in $\mathrm{m} / \mathrm{s}$ of the water flowing in the pipe.

Assertion(A): A solid sphere and a hollow sphere both of same material are immersed in a liquid, then change in weight in both the spheres will be same.

Reason(R): Upthrust depends upon the volume of the solid immersed not the mass.

A small block of wood of specific gravity 0.5 is submerged at a depth of $1.2 \mathrm{~m}$ in a vessel filled with water. The vessel is accelerated upwards with an acceleration $a_0=\frac{g}{2}$. Time taken by the block to reach the surface, if it is released with zero initial velocity is $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$

We have two (narrow) capillary tubes ${T_1}$and${T_2}$. Their lengths are${l_1}$ and ${l_2}$and radii of cross-section are ${r_1}$ and ${r_2}$ respectively. The rate of flow of water under a pressure difference $P$ through tube ${T_1}$ is $8c{m^3}/\sec$ . If ${l_1} = 2{l_2}$ and${r_1} = {r_2}$, what will be the rate of flow when the two tubes are connected in series and pressure difference across the combination is same as before $\left( { = P} \right)$

Statement I: A ship floats higher in water on a high
pressure day than on a low pressure day.
Statement II: Floating of ship in the water is possible
because of the buoyant force which is present due to the
pressure difference.

A small spherical ball of steel falls through a viscous medium with terminal velocity $v$. If a ball of twice the radius of the first one but of the same mass is dropped through the same method, it will fall with a terminal velocity (neglect buoyancy)

Water rises up to a height of 12 cm into a capillary tube when placed vertically. If it is now tilted through $45^\circ$ from the vertical, length of the water in the capillary tube is

Two rain drops reach the earth with different terminal velocities having ratio 9:4. Then the ratio of their volume is

A balloon of volume $1500{\mathrm{m}^3}$ and weighing 1650 kg with all its equipment is filled with He (density$0.2\mathrm{kg}{\mathrm{m}^{ - 3}}$. If the density of air be $1.3\mathrm{kg}{\mathrm{m}^{ - 3}}$, the pull on the rope tied to the balloon will be

A liquid rises in a vertical tube. The relation between the weight of the liquid in the tube, surface tension of the liquid $T$ and radius of the tube $r$ is given by (if the angle of contact is zero)

When a pinch of salt or any other salt which is soluble in water is added to water, its surface tension

An iceberg is floating in water. The density of ice in the iceberg is $917\mathrm{kg}{\mathrm{m}^{ - 3}}$ and the density of water is $1024\mathrm{kg}{\mathrm{m}^{ - 3}}$

Water is flowing through a horizontal pipe of varying cross-section. If the pressure of water equals 2 cm of mercury, where the velocity of the flow is $32\mathrm{cm}{\mathrm{s}^{ - 1}}$, what is the pressure at another point, where the velocity of flow is $65\mathrm{cm}{\mathrm{s}^{ - 1}}$ ?

The venturi-meter works on

A weightless bag is filled with 5 kg of water and then weighed in water. The reading of spring balance is

By inserting a capillary tube upto a depth$l$ in water, the water rises to a height$h$. If the lower end of the capillary tube is closed inside water and the capillary is taken out and closed end opened, to what height the water will remain in the tube, when $l > h$?

A glass plate is partly dipped vertically in the mercury and the angle of contact is measured. If the plate is inclined, then the angle of contact will

A cylindrical vessel filled with water upto a height $h$ weighs $w$ and is resting on a horizontal plane. The side of wall of the vessel has a plugged circular hole touching the bottom. The coefficient of friction between the bottom of the vessel and the plane is $\mu$. The minimum diameter of the hole so that the vessel just begins to move on the floor after the removal of the plug is:

A stone of mass $10 \mathrm{~kg}$ is lying at the bed of a large lake $10 \mathrm{~m}$ deep. If the relative density of the stone is 2, the amount of work done by external force to bring slowly it at the surface of the lake will be (neglect all resistive forces)

Statement-1: A block floats in water with some part outside water. When whole system is given a constant upward acceleration then volume of block inside water remains unchanged in equilibrium.
Statement-2: Net force on block in both cases is zero.

An iron block is on a boat which floats in a pond. The block is thrown into the water. The level of water in the pond will be

Statement A: To float a body, weight of the displaced liquid is equal to the actual weight of the body.
Statement B: The body will experience no net downward force in that case.

Rain drops of radius ' $r$ ' having a mass ' ${m}$ ' is falling with terminal velocity. The rate of energy dissipation due to viscous force is proportional

What is 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 the freely falling body? (The densities of metal and of liquid are $\rho$ and $\sigma$ respectively, and the viscosity of the liquid is ɳ)

A sphere of relative density $\sigma$ and diameter $D$ has concentric cavity of diameter ${d}$. The ratio of $\frac{{D}}{{d}}$, if it just floats on water in a tank is:

A piston of cross-section area $100c{m^2}$ is used in a hydraulic press to exert a force of ${10^7}$ dynes on the water. The cross-sectional area of the other piston which supports an object having a mass $2000\mathrm{kg}$. is

The cylindrical tube of spray pump has a cross-section of 8$\mathrm{c}{\mathrm{m}^2}$, one end of which has 40 fine holes each of area ${10^{ - 8}}{\mathrm{m}^2}$. If liquid flows inside the tube with a speed of $0.15\mathrm{m\,\, mi}{\mathrm{n}^{ - 1}}$, the speed with which the liquid is ejected through the hole is