Properties of Matter

A $200 \mathrm{g}$ solid block of Aluminium (Density of Al = $2.70 \mathrm{g}/\mathrm{cc}$) is placed in a beaker of water filled to the brim. Some water overflows. The same is done in another beaker with a $200 \mathrm{g}$ solid block of lead (Density of lead = $11.3 \mathrm{g}/\mathrm{cc}$). Does the block of lead displace more, less, or the same amount of water as the aluminium block?

A $200$ g solid block of Aluminium (Density of Al = $2.70$ g/cc) is placed in a beaker of water filled to the brim. Some water overflows. The same is done in another beaker with a $800$ g solid block of lead (Density of lead = $11.3$ g/cc). Does the block of lead displace more, less, or the same amount of water as the aluminium block?

A cork of density $0.5 \mathrm{g} {\mathrm{cm}}^{-3}$ floats on a calm swimming pool. The fraction of the cork's volume which is under water is

Two bodies having volumes $V$ and $2V$ are suspended from the two arms of a common balance and they are found to balance each other. If larger body is immersed in oil (density $d_1=0.9 \mathrm{g} {\mathrm{cm}}^{-3}$) and the smaller body is immersed in an unknown liquid, then the balance remain in equilibrium. The density of unknown liquid is given by

Some liquid is filled in a cylindrical vessel of radius $R$. Let $F_1$_​ be the force applied by the liquid on the bottom of the cylinder. Now the same liquid is poured into a vessel of uniform square cross-section of side $R$. Let $F_2$ be the force applied by the liquid on the bottom of this new vessel. Then

Calculate the rate of flow of glycerine of density $1.25\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ through the conical section of a pipe if the radii of its ends are $0.1 \mathrm{m} \& 0.04 \mathrm{m}$ and the pressure drop across its length is $10 \mathrm{N} {\mathrm{m}}^{-2}$

Water rises to a height of $10 \mathrm{cm}$ in a capillary tube and mercury falls to a depth of $3.5 \mathrm{cm}$ in the same capillary tube. If the density of mercury is $13.6 \mathrm{gm} {\mathrm{cc}}^{-1}$ and its angle of contact is $135°$ and density of water is $1 \mathrm{gm} {\mathrm{cc}}^{-1}$ and its angle of contact is $0°$, then the ratio of surface tensions of the two liquids is $(\cos 135°=0.7)$

An expansible ballon filled with air floats on the surface of a lake with 2/3 of its volume submerged. How deep must it be sunk in the water so that it is just in equilibrium neither sinking further nor rising ? It is assumed that the temperature of the water is constant & that the height of the water barometer is 9 meters

In air an object weighs 15N, when immersed completely in water the same object weighs 12N. When immersed in another liquid completely, it weighs 13N. Find the specific gravity of the object.

A film of water is formed between two straight parallel wires of length $10 \mathrm{cm}$ each separated by $0.5 \mathrm{cm}$. if their separation is increased by $1 \mathrm{mm}$ while still maintaining their parallelism, how much work will have to be done (surface tension of water $= 7.2\times {10}^{-2} \mathrm{N} {\mathrm{m}}^{-1}$)

A liquid film is formed over a frame $ABCD$ as shown in figure. Wire $CD$ can slide without friction. The mass to be hung from $CD$ to keep it in equilibrium is

There is horizontal film of soap solution. On it a thread is placed in the form of a loop. The film is pierced inside the loop and the thread becomes a circular loop of radius $R$. If the surface tension of the loop be $T$ , then what will be the tension in the thread​

A $10 \mathrm{cm}$ long wire is placed horizontally on the surface of water and is gently pulled up with a force of  $2\times {\mathrm{10}}^{-2} \mathrm{N}$ to keep the wire in equilibrium. The surface tension in  $\mathrm{N} {\mathrm{m}}^{-1}$ of water is

A wooden stick $2 \mathrm{m}$ long is floating on the surface of water. The surface tension of water $0.07 \mathrm{N} {\mathrm{m}}^{-1}$. By putting soap solution on one side of the stick, the surface tension is reduced to $0.06 \mathrm{N} {\mathrm{m}}^{-1}$. The net force on the stick will be

A small cuboid of mass $1200 \mathrm{g}$ floats on water with its surface$\left(8 \mathrm{cm}\times 4 \mathrm{cm}\right)$ getting wet by the water completely. If the distance (in $\mathrm{cm}$) through which the cuboid is displaced only because of the presence of surface tension is $3755\times {10}^{-x}$, then find $x$. (Surface tension of water $=0.07 \mathrm{N} {\mathrm{m}}^{-1}, g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and density of cuboid $=2500 \mathrm{kg} {\mathrm{m}}^{-3}$)

An incompressible liquid is flowing through a horizontal tube in streamline manner as shown in figure. The value of $h$ is (in meters)

A solid cube floats in water half immersed and has small vertical oscillations of time period $\frac{\pi }{5}$ seconds. Its mass (in $\mathrm{kg}$) is (Take, $\mathrm{g}=10{ \mathrm{ms}}^{-2}$)

A liquid of density $\rho$ is forced out through a small hole by means of a piston of cross-section '$A$', on which a force $F$ is applied. The flow is streamline. The liquid stream strikes the ground at a distance '$x$' in front of the hole. The hole is in the middle of the right face and its height is '$h$' above the ground. The expression for $x^2$ is:

Arrangement of pipes carrying fluids of densities ${\rho }_1, {\rho }_2\text{ \& }{\rho }_3$ is shown in the figure below. If the pipe carrying fluid of density ${\rho }_1$ makes an angle $\theta$ with the horizontal, then what is the value of $\prime h\prime$?

A solid object having uniform density $\left(\rho \right)$ and varying cross-sectional area (which is circular) is placed on smooth horizontal surface as shown. Then the value of $\frac{R_1}{R_2}$ if the stress throughout its height remains same and having value equal to $\mathrm{c}$.