Properties of Matter

Water flows in a streamline motion through a horizontal pipe of circular cross-section as shown in the figure. The pressure difference of water between $P$ and $Q$ is $15 \mathrm{Nm}^{-2}$. The area of cross-section at $P$ and $Q$ are $40 \...

In the measurement of viscosity of liquids using terminal velocity experiment, spherical balls of same radius but having different densities are used. The variation of the terminal velocity ( $v$ ) with the ratio of density of spherical bal...

A submarine is designed to withstand an absolute pressure of 100 atm . How deep can it go below the water surface?
(Consider the density of water $=1000 \mathrm{~kg} \mathrm{~m}^{-3}$, $1 \mathrm{~atm}=1 \times 10^5 \mathrm{~Pa}$ and gravit...

\(\text { Match List I with List II: }\)


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Consider a water tank shown in the figure. It has one wall at $x=L$ and can be taken to be very wide in the $z$ direction. When filled with a liquid of surface tension $S$ and density $\rho$, the liquid surface makes angle $\theta_0\left(\t...

An ideal fluid is flowing in a non-uniform cross-sectional tube \(X Y\) (as shown in the figure) from end \(X\) to end \(Y\). If \(K_1\) and \(K_2\) are the kinetic energy per unit volume of the fluid at \(X\) and \(Y\) respectively, then t...

A thin flat circular disc of radius \(4.5 \mathrm{~cm}\) is placed gently over the surface of water. If surface tension of water is \(0.07 \mathrm{~N} \mathrm{~m}^{-1}\), then the excess force required to take it away from the surface is

The maximum elongation of a steel wire of \(1 \mathrm{~m}\) length if the elastic limit of steel and its Young's modulus, respectively, are \(8 \times 10^8 \mathrm{~N} \mathrm{~m}^{-2}\) and \(2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\)...

A metallic bar of Young's modulus, \(0.5 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\) and coefficient of linear thermal expansion \(10^{-5}{ }^{\circ} \mathrm{C}^{-1}\), length \(1 \mathrm{~m}\) and area of cross-section $$10^{-3} \mathrm{...

The viscous drag acting on a metal sphere of diameter \(1 \mathrm{~mm}\), falling through a fluid of viscosity \(0.8 \mathrm{~Pa}\) s with a velocity of \(2 \mathrm{~m} \mathrm{~s}^{-1}\) is equal to :

Which of the following statement is not true?

The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length \(100 \mathrm{~cm}\) to stretch it by \(1 \mathrm{~mm}\) is (if Young's modulus of the wire \(=2.0 \times 10^{11} \mathrm{Nm}^{-2}\) ) :

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight \(W\) attached at its free end. The longitudinal stress at any point of cross-sectional area \(A\) of the wire is :

The venturi-meter works on :

The amount of energy required to form a soap bubble of radius \(2 \mathrm{~cm}\) from a soap solution is nearly: (surface tension of soap solution \(=0.03 \mathrm{~N} \mathrm{~m}^{-1}\) )

The terminal velocity of a copper ball of radius 5 mm falling through a tank of oil at room temperature is 10 cm s\(-\)1. If the viscosity of oil at room temperature is 0.9 kg m\(-\)1 s\(-\)1, the viscous drag force is :

Two copper vessels A and B have the same base area but of different shapes. A takes twice the volume of water as that B requires to fill upto a particular common height. Then the correct statement among the following is :

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The stretching of a spring is determined by the shear modulus of the material of the spring.
Reason (R) : A coil spri...

If a soap bubble expands, the pressure inside the bubble

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 (v) as a function of time (t) is

The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerin becomes constant after some time. If the density of glycerin is \({d \over 2}\), then the viscous force acting on the ball will be :

A wire of length L, are of cross section A is hanging from a fixed support. The length of the wire changed to L1 when mass M is suspended from its free end. The expression for Young's modulus is :

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 5 g. Another capillary tube of radius 2r is immersed in Water. The mass of water that will rise in this tube is...

A small hole of area of cross-section 2 mm2 present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/s2, the rate of flow of water through the open hole would be nearly :

The unit of thermal conductivity is :

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L + \(l\)). The elastic potential energy stored in the extended wire is :

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in tmperature. The length of aluminium rod is : (\(\alpha\)Cu = 1.7 × 10–5 K–1 and
\(\alpha\)Al = 2.2 × 10–5 K–1)

A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 \(\times\) 10–2 N/m. The pressure inside the bubble equals at a point Z0 below the free surface of water in a container. Taking g = 1...

Two wires are made of the same material and
have the same volume. The first wire has
cross-sectional area A and the second wire has
cross-sectional area 3A. If the length of the first
wire is increased by \(\Delta\)l on applying a force F,...

A small sphere of radius ‘r’ falls from rest in a
viscous liquid. As a result, heat is produced
due to viscous force. The rate of production of
heat when the sphere attains its terminal velocity,
is proportional to

The power radiated by a black body is P and it
radiates maximum energy at wavelength, \(\lambda\)0
. If
the temperature of the black body is now
changed so that it radiates maximum energy at
wavelength \({3 \over 4}{\lambda _0}\), the powe...

A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be

The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'P', the fractional decrease in radius is

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite will be

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 mm above the water level on the other side. Meanwhile the wate...

A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be

A rectangular film of liquid is extended from (4 cm \(\times\) 2 cm) to (5 cm \(\times\) 4 cm). If the work done is 3 \(\times\) 10\(-\)4 J, the value of the surface tension of the liquid is

Three liquids of densities \(\rho\)1, \(\rho\)2  and \(\rho\)3 (with \(\rho\)1 > \(\rho\)2 > \(\rho\)3), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact $$\thet...

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at 100oC, while the other one is at 0oC. If the two bodies are brought into contact, then, assuming no heat loss, the final ...

A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is U1, at wavelength 500 nm is U2 and that at 1000 nm is U3. Wien's constant, b = 2.88 \(\times\) 106 nm K. Which of the followin...

Two non-mixing liquids of densities \(\rho\) and n\(\rho\) (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and...

Coefficient of linear expansion of brass and steel rods are \(\alpha\)1 and \(\alpha\)2. Lengths of brass and steel rods are \(l\)1 and \(l\)2 respectively. If (\(l\)1 \(-\) \(l\)2) is maintained same at all temperatures, which one of the...

A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h [Latent heat of ice is $$3.4 \time...

The two ends of a metal rod are maintained at temperatures 100oC and 110oC. The rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures 200oC and 210oC, the rate of heat flow will be

The approximate depth of an ocean is 2700 m. The compressiblity of water is 45.4 \(\times\) 10\(-\)11 Pa\(-\)1 and density of water is 103 kg/m3. What fractional compression of water will be obtained at the bottom of the ocean?

A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m2. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force wi...

On observing light from three different starts P, Q and R, it was found that intensity of violet colour is maximum in the spectrum of P, the intensity of green colour is maximum in the spectrum of R and the intensity of red colour is maximu...

Water rises to a height h in capillary tube. If the length of capillary tube above the surface of water is made less than h, then

The value of coefficient of volume expansion of glycerin is 5 \(\times\) 10\(-\)4 K\(-\)1. The fractional change in the density of glycerin for a rise of 40oC in its temperature, is

The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same le...