Properties of Matter

A container of height 2 m , length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates ( $\mathrm{M}_1$ and $\mathrm{M}_2$ ) which extend far beyond the vertical walls in all directions. The c...

A table tennis ball has radius $(3 / 2) \times 10^{-2} \mathrm{~m}$ and mass $(22 / 7) \times 10^{-3} \mathrm{~kg}$. It is slowly pushed down into a swimming pool to a depth of $d=0.7 \mathrm{~m}$ below the water surface and then released f...

Two large, identical water tanks, 1 and 2 , kept on the top of a building of height $H$, are filled with water up to height $h$ in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A ...

An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius $0.1 \mathrm{~mm}$ is dipped vertically into the liquid through the airtight piston hole, as shown in the figure. The a...

A bubble has surface tension $S$. The ideal gas inside the bubble has ratio of specific heats $\gamma=$ $\frac{5}{3}$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $P_{a...

An ideal gas of density $\rho=0.2 \mathrm{~kg} \mathrm{~m}^{-3}$ enters a chimney of height $h$ at the rate of $\alpha=$ $0.8 \mathrm{~kg} \mathrm{~s}^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The c...

A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration a along a fixed inclined plane with angle \(\theta\) = 45\(^\circ\). P1 and P2 are pressures at points 1 and 2, r...

A train with cross-sectional area St
is moving with speed vt
inside a long tunnel of cross-sectional
area S0 (S0 = 4St). Assume that almost all the air (density \(\rho\)) in front of the train flows back between
its sides and the walls of ...

A cubical solid aluminium (bulk modulus = \(- V{{dP} \over {dV}} = 70GPa\)) block has an edge length of 1 m on the surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the average density of water and the acceleration...

A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total
mass is 480 kg. Its effective volume giving the balloon its buoyancy is V. The balloon is floating at
an equilibrium height of 100 m. When...

As shown schematically in the figure, two vessels contain water solutions (at temperature T) of
potassium permanganate (KMnO4) of different concentrations n1 and n2 (n1 > n2) molecules per
unit volume with \(\Delta\)n = (n1 − n2) << n1. Wh...

An open-ended U-tube of uniform cross-sectional area contains water (density 103 kg m−3
). Initially the
water level stands at 0.29 m from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of
density 800 kg m−3
is added to th...

When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to
the surface tension of water. To calculate h just before water starts flowing, model the shape of the
water above the rim as a disc o...

A block of weight 100 N is suspended by copper and steel wires of same cross-sectional area 0.5 cm2 and length \(\sqrt 3\) m and 1 m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper ...

A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T1 and T2 of different materials having water contact angles of 0\(^\circ\) and 60\(^\circ\), respectively. The capillary tube is dipped vertically in water ...

A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as $$T(t) = {T...

A liquid at 30\(^\circ\)C is poured very slowly into a Calorimeter that is at temperature of 110\(^\circ\)C. The boiling temperature of the liquid is 80\(^\circ\)C. It is found that the first 5 gm of the liquid completely evaporates. Aft...

Consider a thin square plate floating on a viscous liquid in a large tank. The height \(h\) of the liquid in the tank is much less than the width of the tank. The floating place is pulled horizontally with a constant velocity $${\mu _{0.}}$...

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures \({T_1} = 300\,K\) and \({T_2} = 100\,K\), as shown in the figure. The radius of the bigger cylinder is twice t...

A uniform capillary tube of inner radius \(r\) is dipped vertically into a beaker filled with water. The water rises to a height \(h\) in the capillary tube above the water surface in the beaker. The surface tension of water is \(\sigma .\)...

A human body has a surface area of approximately \(1\,m{}^2.\) The normal body temperature is \(10\) \(K\) above the surrounding room temperature \({T_0}.\) Take the room temperature to be \({T_0} = 300K.\) For \({T_0} = 300\,K,\) the value...

A drop of liquid of radius \(R = {10^{ - 2}}\,m\) having surface tension \(S = {{0.1} \over {4\pi }}N{m^{ - 1}}\) divides itself into \(K\) identical drops. In this process the total change in the surface energy $$\Delta U = {10^{ - 3}}\,J...

Consider two solid spheres P and Q each of density 8 gm cm–3 and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm–3 and viscosity \(\eta\) = 3 poiseulles. Sphere Q is dropped into a liquid of ...

A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the pressure at r (r < R), then the correct option(s) is(are)

Two spheres P and Q for equal radii have densities \(\rho\)1 and \(\rho\)2, respectively. The spheres are connected by a massless string and placed in liquids L1 and L2 of densities \(\sigma\)1 and \(\sigma\)2 and viscosities \({\eta _1}\) ...

In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then, the correct statements is/are

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is
at rest, the water jet coming out of the hole hits the floor of the lift at a distance d of 1.2 m from the person.
In the follo...

If the density of air is \(\rho\)a and that of the liquid \(\rho\)l, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to

If the piston is pushed at a speed of 5 mm s\(-\)1, the air comes out of the nozzle with a speed of

A glass capillary tube is of the shape of truncated cone with an apex angle \(\alpha\) so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height h, where the radius of its cr...

Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5 kg water by 40 K. This heater is replaced by a new heater having two wires of the same material, each of length L ...

A solid sphere of radius R and density \(\rho\) is attached to one end of a mass-less spring of force constant k.
The other end of the spring is connected to another solid sphere of radius R and density 3\(\rho\). The complete
arrangement...

One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another
horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces
at two ends, the ratio of the elo...

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating
vertically in water in half-submerged state. If \({\rho _c}\) is the relative density of the material of the shell
with respect to water, ...

A person blows into the open end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,

Two solid spheres A and B of equal volumes but of different densities dA and dB are connected by a string. They are fully immersed in a fluid of density dF. They get arranged into an equilibrium state as shown in the figure with a tension i...

A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat Q flows only from lef...

When liquid medicine of density \(\rho\) is to be put in the eye, it is done with the help of a dropper. As the bulb on the
top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop...

When liquid medicine of density \(\rho\) is to be put in the eye, it is done with the help of a dropper. As the bulb on the
top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop...

When liquid medicine of density \(\rho\) is to be put in the eye, it is done with the help of a dropper. As the bulb on the
top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop...

A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. ...

Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m\(^2\). The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04 N/m. Fin...

A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as s...

The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)

When the gas bubble is at a height y from the bottom, its temperature is :

As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

STATEMENT - 1 :
The stream of water flowing at high speed from a garden hose pipe tends to spread line a fountain when held vertically up, but tends to narrow down when held vertically down.
and
STATEMENT - 2 :
In any steady flow of an inco...

Column I gives some devices and Column II gives some process on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the $$...

Water is filled up to a height \(h\) in a beaker of radius \(R\) as shown in the figure. The density of water is \(\rho\), the surface tension of water is \(T\) and the atmospheric pressure is P. Consider a vertical section \(A B C D\) of t...

Let the cylinder is prevented from moving up, by applying a force and water level is further decreased. Then, the height of water level ( $h_2$ in the figure) for which the cylinder remains in original position without application of force ...