The maximum length of water column that can stay without falling in a vertically held capillary tube of diameter 1 mm and open at both the ends is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ and surface tension of water $=0.07 \mathrm{Nm}^{-1}$ )

A wooden block of outer volume 1 litre and specific gravity $\frac{3}{4}$ having a cavity floats with half of its volume immersed in water. Then, the volume of the cavity is

Due to the presence of air resistance, if a body dropped from a height of 20 m reaches the ground with a speed of $18 \mathrm{~ms}^{-1}$, then the time taken by the body to reach the ground is nearly

A thin film of water is formed between two straight parallel wires each of length 8 cm separated by distance of 0.6 cm . The work done to increase the distance between the wires to 0.8 cm is (Surface tension of water $=0.07 \mathrm{Nm}^{-1}$ )

A rain drop of diameter 1 mm falls with a terminal velocity of $0.7 \mathrm{~ms}^{-1}$ in air. If the coefficient of viscosity of air is $2 \times 10^{-5} \mathrm{~Pa}$-s, the viscous force on the rain drop is

An air bubble rises from the bottom to the top of a water tank in which the temperature of the water is uniform. The surface area of the bubble at the top of the tank is $125 \%$ more than its surface area at the bottom of the tank. If the atmospheric pressure is equal to the pressure of 10 m water column, then the depth of water in the tank is

If $W_1$ is the work done in increasing the radius of a soap bubble from ' $r$ ' to ' $2 r$ ' and $W_2$ is the work done in increasing the radius of the soap bubble from ' $2 r$ ' to ' $3 r$ ', then $W_1: W_2=$

Water is filled in a tank up to a height of 20 cm from the bottom of the tank. Water flows through a hole of area $1 \mathrm{~mm}^2$ at its bottom. The mass of the water coming out from the hole in a time of 0.6 s is

For which of the following Reynold's number, a flow is streamlined?

The work done in blowing a soap bubble of diameter 3 cm is (surface tension of soap solution $=0.035 \mathrm{Nm}^{-1}$ )

If the terminal velocity of a metal sphere of mass 8 g falling through a liquid is $3 \mathrm{cms}^{-1}$, then the terminal velocity of another sphere of mass 64 g made of the same metal falling through same liquid is

When a large bubble rises from the bottom of a lake to the surface, the volume of the bubble becomes 5 times its volume at the bottom of the lake. If $H$ is the atmospheric pressure expressed in terms of water column height, then the depth of the lake is

(The temperature of the water in the lake is same at all points)

A water drop breaks into 64 identical droplets of each surface area $10^{-7} \mathrm{~m}^2$. If the surface tension of water is $0.07 \mathrm{Nm}^{-1}$, the increase in the surface energy in the process is

A cylindrical vessel, open at the top, contains 15 litres of water. Water drains out through a small opening at the bottom. 5 litre of water comes out in time $t_1$, the next 5 litre in further time $t_2$, and the last 5 litre in further time $t_3$, Then

A cylinder of mass $m$ and material density $\rho$ hanging from a string is lowered into a vessel of cross-sectional area $A$ containing a liquid of density $\sigma(<\rho)$ until it is fully immersed. The increase in pressure at the bottom of the vessel is

The angle of contact is $120^{\circ}$ when a cylindrical rod is vertically placed in a liquid. If the same rod is placed horizontally in the liquid, then the angle of contact is

In a well the pressure at a point 10 m below the surface of water is $\left(g=10 \mathrm{~ms}^{-2}\right)$

A liquid is taken in a long vertical cylindrical vessel and the cylinder is rotated about its vertical axis as shown in figure. During rotation, the liquid rises along its sides. If the radius of vessel is 0.05 m and speed of rotation is $10 \mathrm{rads}^{-1}$, then the height difference between the liquid at the centre of the vessel and its sides is $\left(g=10 \mathrm{~ms}^{-2}\right)$

A vessel having small hole in the bottom has to hold water without leakage, if water is poured into if upto a height of 7 cm . Then the radius of the hole is (surface tension of water is $0.07 \mathrm{Nm}^{-1}$, angle of contact is $0^{\circ}$ and $g=10 \mathrm{~ms}^{-2}$ )

If the work done in blowing a soap bubble of radius $R$ is $W$, then the work done in blowing the soap bubble of radius $2 R$ is

Three identical vessels are filled with three liquids ${ }_{A, B}$ and $C$ with equal masses but having densities $\rho_{A, \rho_B}$ and $\rho_C$ respectively. If $\rho_A>\rho_B>\rho_C$ then the pressure at the bottom of the vessels will be

A wide cylindrical vessel 50 cm in height is filled with water and rests on a table. Assuming the viscosity to be negligible. Find at what height from the bottom of the vessel a small hole should be made for the water jet coming out of it to hit the surface of the table at the maximum horizontal distance from the vessel

A spherical drop of radius $r$ is divided into 8 equal droplets. If the surface tension is $S$, then the work done in the process will be

A venturimeter has a pipe diameter of 4 cm and a throat diameter of 2 cm . Velocity of water in the pipe section is $10 \mathrm{~m} / \mathrm{s}$. The pressure drop, between pipe section and the throat section is (use, density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$ )

A soap bubble of initial radius $R$ is to be blown up. The surface tension of the soap film is $T$. The surface energy needed to double the diameter of the bubble is

Consider an increase of $1 \%$ in each of radius of artery, viscosity of blood and density of blood, respectively. The percentage change in flow rate of blood in artery is

A metal cube of side 10 cm rests on a film of a liquid of thickness 0.2 mm . If upon applying a horizontal force $\mathbf{F}$ of magnitude 0.1 N . The cube slides with a constant speed of $0.08 \mathrm{~m} / \mathrm{s}$, then the coefficient of viscosity is

In the figure, the chamber $A$ contains a gas, movable chamber $B$ is placed on the top of the gas and it contains $n$ metal balls. The weight of chamber $B$ is supported by the gas. Chamber $C$ has vacuum. Let the gas be in equilibrium at pressure $p$. Let $p^{\prime}$ be the pressure, if one of the balls is taken away. Find $\left(p-p^{\prime}\right) / p$.

A liquid flows steadily through a cylindrical pipe having a radius $2 R$ at a point $A$ and radius $R$ at point $B$ farther along the flow direction. If the velocity at point $B$ is $4 v$, what will be the velocity at point $A$ ?

A hollow spherical body of outer and inner radii of 4 cm and 2 cm respectively, floats half submerged in a liquid of density $2.0 \mathrm{~g} / \mathrm{cm}^3$. The density of the material of the sphere is

What is the terminal velocity of a rain drop of radius 0.02 mm ?

[Note that the coefficient of viscosity of air is $1.8 \times 10^{-5} \mathrm{N} / \mathrm{m}^2$, density of water is $1000 \mathrm{~kg} / \mathrm{m}^3$. Use, $g=10 \mathrm{~m} / \mathrm{s}^2$ and density of air can be neglected in comparision with density of water]

A large storage tank, open to the atmosphere at top and filled with water, develops a small hole in its side at a point 20.0 m below the water level. If the rate of flow from the hole is $3.08 \times 10^{-5} \mathrm{~m}^3 / \mathrm{s}$, then the diameter of the hole is (take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

An air bubble of radius 1 mm is at a depth of 8 cm below the free surface of a liquid column. If the surface tension and density of the liquid is $0.1 \mathrm{~N} / \mathrm{m}$ and 2000 $\mathrm{kg} / \mathrm{m}^3$, respectively, by what amount is the pressure inside the bubble greater than the atmospheric pressure? (take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

The change in surface energy when a big spherical drop fo radius $R$ is split into $n$ spherical droplets of radius $r$ is ( $T=$ surface tension)

A hydraulic lift as shown in the figure is used to lift a mass of 1000 kg , which is placed on a piston $\left(P_1\right)$ of area $1 \mathrm{~m}^2$. If the cross-section area of the piston $\left(P_2\right)$ at the other end is $0.01 \mathrm{~m}^2$, then how much mass needs to be put on it to lift the 1000 kg ?

A cubical block of wood having mass of 160 g has a metal piece fastened underneath as shown in the figure. Find the maximum mass of the metal piece which will allow the block to float in water. Specific gravity of wood is 0.8 and that metal is 10 and density of water $=1 \mathrm{~g} / \mathrm{cc}$.

A meniscus drop of radius 1 cm is sprayed into $10^6$ droplets of equal size. Calculate the energy expended if surface tension of mercury is $435 \times 10^{-3} \mathrm{~N} / \mathrm{m}$.