A cubical block of density $\rho_b=600 \mathrm{~kg} / \mathrm{m}^3$ floats in a liquid of density $\rho_{\mathrm{e}}=900 \mathrm{kg} / \mathrm{m}^3$. If the height of block is $H=8.0 \mathrm{~cm}$ then height of the submerged part is

$\_\_\_\_$ cm .

A brass wire of length 2 m and radius 1 mm at $27^{\circ} \mathrm{C}$ is held taut between two rigid supports. Initially it was cooled to a temperature of $-43^{\circ} \mathrm{C}$ creating a tension $T$ in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to $1.4 T$, is $\_\_\_\_$ ${ }^{\circ} \mathrm{C}$.

A small metallic sphere of diameter 2 mm and density $10.5 \mathrm{~g} / \mathrm{cm}^3$ is dropped in glycerine having viscosity 10 Poise and density $1.5 \mathrm{~g} / \mathrm{cm}^3$ respectively. The terminal velocity attained by the sphere is $\_\_\_\_$ $\mathrm{cm} / \mathrm{s}$.

$\left(\pi=\frac{22}{7}\right.$ and $\left.g=10 \mathrm{~m} / \mathrm{s}^2\right)$

The strain-stress plot for materials $A, B, C$ and $D$ is shown in the figure. Which material has the largest Young's modulus ?

When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height $h$. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by $1 \%$ each, then the height of the liquid in the tube will change by $\_\_\_\_$ $\%$.

Given below are two statements :

Statement I : Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.

Statement II : Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.

In the light of the above statements, choose the correct answer from the options given below

Surface tension of two liquids (having same densities), $T_1$ and $T_2$, are measured using capillary rise method utilizing two tubes with inner radii of $r_1$ and $r_2$ where $r_1 > r_2$. The measured liquid heights in these tubes are $h_1$ and $h_2$ respectively. [Ignore the weight of the liquid above the lowest point of miniscus]. The heights $h_1$ and $h_2$ and surface tensions $T_1$ and $T_2$ satisfy the relation :

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at $30^{\circ} \mathrm{C}$. The coefficient of linear expansion of aluminium and steel are $24 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $1.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}$, respectively. The length of this composite rod when its temperature is raised to $100^{\circ} \mathrm{C}$, is $\_\_\_\_$ cm.

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at $A$ and $B$ are $6 \mathrm{~cm}^2$ and $3 \mathrm{~cm}^2$ respectively. The rate of flow will be $\_\_\_\_$ $\mathrm{cm}^3 / \mathrm{s}$. (take $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A liquid of density $600 \mathrm{~kg} / \mathrm{m}^3$ flowing steadily in a tube of varying cross-section. The cross-section at a point $A$ is $1.0 \mathrm{~cm}^2$ and that at $B$ is $20 \mathrm{~mm}^2$. Both the points $A$ and $B$ are in same horizontal plane, the speed of the liquid at $A$ is $10 \mathrm{~cm} / \mathrm{s}$. The difference in pressures at $A$ and $B$ points is $\_\_\_\_$ Pa.

A spherical liquid drop of radius $R$ acquires the terminal velocity $v_1$ when falls through a gas of viscosity $\eta$. Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity $v_2$ falling through the same gas. The ratio of terminal velocities $v_1 / v_2$ is $\_\_\_\_$ .

Figure represents the extension $(\Delta l)$ of a wire of length 1 meter, suspended from the ceiling of the room at one end with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-5} \mathrm{~m}^2$ then the Young's modulus of the wire is $\_\_\_\_$ $\mathrm{N} / \mathrm{m}^2$.

A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is $528 \mathrm{dm}^3$ (dm : decimeter) The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm below the top of water level, then horizontal range of water falling on the ground in the beginning is $\_\_\_\_$ cm .

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is $4 \times 10^8 \mathrm{~N} / \mathrm{m}^2$ and its radius is 4 mm , then maximum acceleration the lift can take is $\_\_\_\_$ $\mathrm{m} / \mathrm{s}^2$.

(take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ and $\pi=3.14$ )

The two wires $A$ and $B$ of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire $A$ and wire $B$ is 20/11. When the joined wire is kept under certain tension the elongations in the wires $A$ and $B$ are equal. If the length of wire $A$ is 2.2 m , then the length of wire $B$ is

$\_\_\_\_$ m.

Eight mercury drops, each of radius $r$, coalesce to form a bigger drop. The surface energy released in this process is $\_\_\_\_$ - ( $S$ is the surface tension of mercury).

The Young's modulus of steel wire of radius $r$ and length $L$ is $Y$.

If the radius $r$ and length $L$ of the wire are doubled then the value of $Y$

Two wires as shown in the figure below, made of steel and have breaking stress of $12 \times 10^8 \mathrm{~N} / \mathrm{m}^2$. Area of cross-section of upper wire is $0.008 \mathrm{~cm}^2$ and of lower wire is $0.004 \mathrm{~cm}^2$. The maximum mass that can be added to pan without breaking any wire is $\_\_\_\_$ kg.

A metal string $A$ is suspended from a rigid support and its free end is attached to a block of mass $M$. Second block having mass 2 M is suspended at the bottom of the first block using a string $B$. The area of cross sections of strings $A$ and $B$ are same. The ratio of lengths of strings of $A$ to B is 2 and the ratio of their Young's moduli $\left(Y_A / Y_B\right)$ is 0.5 . The ratio of elongations in $A$ to $B$ is $\_\_\_\_$ .

A water spray gun is attached to a hose of cross sectional area $30 \mathrm{~cm}^2$. The gun comprises of 10 perforations each of cross sectional area of $15 \mathrm{~mm}^2$. If the water flows in the hose with the speed of $50 \mathrm{~cm} / \mathrm{s}$, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

The increase in the pressure required to decrease the volume ( $\Delta V$ ) of water is $6.3 \times 10^7 \mathrm{~N} / \mathrm{m}^2$. The percentage decrease in the volume is $\_\_\_\_$ .

(Bulk modulus of water $=2.1 \times 10^9 \mathrm{~N} / \mathrm{m}^2$.)

A string $A$ of length 0.314 m and Young's modulus $2 \times 10^{10} \mathrm{~N} / \mathrm{m}^2$ is connected to another string $B$ of length and Young's modulus both twice of those of $A$. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg . The net change in length of the combination is $\_\_\_\_$ mm.

(radius of both the strings is 0.2 mm and acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$ ) (Mass of both strings is to be neglected as compared to the mass of load)

The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is $\alpha \pi \times 10^{-4}$ J. The value of $\alpha$ is _________. (Take $\pi = 3.14$)

If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 kg/m³ at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is ______ Poise. (Take g = 10 m/s²)

A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is $\alpha \times 10^{-6}$ J. The value of $\alpha$ is _______. (Take surface tension of liquid = 0.08 N/m)

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is $P \times 10^{11} \, \text{Nm}^{-2}$, where the value of $P$ is: (Take $g = 3\pi \, \text{m/s}^2$)

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle ≈ 0°) with 30° inclined with the vertical. The length of water risen in the capillary is _______ cm. (Take $g = 9.8 \text{ m/s}^2$)

Two wires A and B are made of same material having ratio of lengths $\frac{L_A}{L_B}=\frac{1}{3}$ and their diameters ratio $\frac{d_A}{d_B}=2$. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of $10^5 \mathrm{~N}$ at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement $\theta$ of the rod axis from its original position would be : (shear moduli, $G=10^{10} \mathrm{~N} / \mathrm{m}^2$ )

Two liquids $A$ and $B$ have $\theta_A$ and $\theta_B$ as contact angles in a capillary tube. If $K=\cos \theta_A / \cos \theta_B$, then identify the correct statement:

A solid steel ball of diameter 3.6 mm acquired terminal velocity $2.45 \times 10^{-2} \mathrm{~m} / \mathrm{s}$ while falling under gravity through an oil of density $925 \mathrm{~kg} \mathrm{~m}^{-3}$. Take density of steel as $7825 \mathrm{~kg} \mathrm{~m}^{-3}$ and g as $9.8 \mathrm{~m} / \mathrm{s}^2$. The viscosity of the oil in SI unit is

Consider a completely full cylindrical water tank of height 1.6 m and of cross-sectional area $0.5 \mathrm{~m}^2$. It has a small hole in its side at a height 90 cm from the bottom. Assume, the crosssectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is:

$ \left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right) $

The fractional compression $\left( \frac{\Delta V}{V} \right)$ of water at the depth of 2.5 km below the sea level is __________ %. Given, the Bulk modulus of water = $2 \times 10^9$ N m$^{-2}$, density of water = $10^3$ kg m$^{-3}$, acceleration due to gravity $g = 10$ m s$^{-2}$.

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water?

(Given: density of water = 1000 kg m^-3)

In the experiment for measurement of viscosity ' $\eta$ ' of given liquid with a ball having radius $R$, consider following statements.

A. Graph between terminal velocity V and R will be a parabola.

B. The terminal velocities of different diameter balls are constant for a given liquid.

C. Measurement of terminal velocity is dependent on the temperature.

D. This experiment can be utilized to assess the density of a given liquid.

E. If balls are dropped with some initial speed, the value of $\eta$ will change.

Choose the correct answer from the options given below:

Consider following statements:

A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid.

B. As the temperature of liquid rises, the coefficient of viscosity increases.

C. As the temperature of gas increases, the coefficient of viscosity increases

D. The onset of turbulence is determined by Reynold's number.

E. In a steady flow two stream lines never intersect.

Choose the correct answer from the options given below:

The amount of work done to break a big water drop of radius ' $R$ ' into 27 small drops of equal radius is 10 J . The work done required to break the same big drop into 64 small drops of equal radius will be

A massless spring gets elongated by amount $x_1$ under a tension of 5 N . Its elongation is $x_2$ under the tension of 7 N . For the elongation of $\left(5 x_1-2 x_2\right)$, the tension in the spring will be,

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$. The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to

Given below are two statements:

Statement I: The hot water flows faster than cold water

Statement II: Soap water has higher surface tension as compared to fresh water. In the light above statements, choose the correct answer from the options given below

A tube of length $L$ is shown in the figure. The radius of cross section at the point $(1)$ is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is $2 \mathrm{~m} / \mathrm{s}$, then velocity of water leaving the point (2) will be

A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

A spherical ball of radius $1 \times 10^{-4} \mathrm{~m}$ and density $10^5 \mathrm{~kg} / \mathrm{m}^3$ falls freely under gravity through a distance $h$ before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of $h$ is approximately:

(The coefficient of viscosity of water is $9.8 \times 10^{-6} \mathrm{~N} \mathrm{~s} / \mathrm{m}^2$)

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 cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil = 0.8, specific gravity of ice = 0.9):

Young's modulus is determined by the equation given by $\mathrm{Y}=49000 \frac{\mathrm{m}}{\mathrm{l}} \frac{\mathrm{dyne}}{\mathrm{cm}^2}$ where $M$ is the mass and $l$ is the extension of wire used in the experiment. Now error in Young modules $(Y)$ is estimated by taking data from $M-l$ plot in graph paper. The smallest scale divisions are $5 \mathrm{~g}$ and $0.02 \mathrm{~cm}$ along load axis and extension axis respectively. If the value of $M$ and $l$ are $500 \mathrm{~g}$ and $2 \mathrm{~cm}$ respectively then percentage error of $Y$ is :

Correct Bernoulli's equation is (symbols have their usual meaning) :

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $\mathrm{R}=$ Radius of bubble, $\mathrm{S}=$ Surface tension of bubble)

A small ball of mass $m$ and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

Match List I with List II :

Choose the correct answer from the options given below :

Given below are two statements :

Statement I : When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be $0^{\circ}$.

Statement II : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.

In the light of the above statement, choose the correct answer from the options given below.

Given below are two statements :

Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.

Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.

In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements :

Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $\mathrm{P}_1-\mathrm{P}_2=\rho g\left(\mathrm{~h}_2-\mathrm{h}_1\right)$.

Statement II : In ventury tube shown $2 \mathrm{gh}=v_1^2-v_2^2$

In the light of the above statements, choose the most appropriate answer from the options given below.

A small spherical ball of radius $r$, falling through a viscous medium of negligible density has terminal velocity '$v$'. Another ball of the same mass but of radius $2 r$, falling through the same viscous medium will have terminal velocity:

A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?

Young's modules of material of a wire of length '$L$' and cross-sectional area $A$ is $Y$. If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be :

A small liquid drop of radius $R$ is divided into 27 identical liquid drops. If the surface tension is $T$, then the work done in the process will be:

A wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$, its length increases by $l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

Given below are two statements:

Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.

Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.

In the light of the above statements, choose the most appropriate from the options given below

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity.

Reason (R) : The restoring force depends upon the bonded inter atomic and inter molecular force of solid.

In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements :

Statement (I) :Viscosity of gases is greater than that of liquids.

Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities.

In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A : A spherical body of radius $(5 \pm 0.1) \mathrm{mm}$ having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is $4 \%$.

Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.

In the light of the above statements, choose the correct answer from the options given below

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at $\mathrm{A}$ is $1.5 \mathrm{~cm}^{2}$, and $\mathrm{B}$ is $25 \mathrm{~mm}^{2}$, if the speed of liquid at $\mathrm{B}$ is $60 \mathrm{~cm} / \mathrm{s}$ then $\left(\mathrm{P}_{\mathrm{A}}-\mathrm{P}_{\mathrm{B}}\right)$ is :

(Given $\mathrm{P}_{\mathrm{A}}$ and $\mathrm{P}_{\mathrm{B}}$ are liquid pressures at $\mathrm{A}$ and $\mathrm{B}$% points.

density $\rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$

$\mathrm{A}$ and $\mathrm{B}$ are on the axis of tube

Under isothermal condition, the pressure of a gas is given by $\mathrm{P}=a \mathrm{~V}^{-3}$, where $a$ is a constant and $\mathrm{V}$ is the volume of the gas. The bulk modulus at constant temperature is equal to

A body cools from $80^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ in 5 minutes. The temperature of the surrounding is $20^{\circ} \mathrm{C}$. The time it takes to cool from $60^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ is :

Eight equal drops of water are falling through air with a steady speed of $10 \mathrm{~cm} / \mathrm{s}$. If the drops coalesce, the new velocity is:-

Young's moduli of the material of wires A and B are in the ratio of $1: 4$, while its area of cross sections are in the ratio of $1: 3$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires $\mathrm{A}$ and $\mathrm{B}$ will be in the ratio of

[Assume length of wires A and B are same]

Given below are two statements:

Statement I : Pressure in a reservoir of water is same at all points at the same level of water.

Statement II : The pressure applied to enclosed water is transmitted in all directions equally.

In the light of the above statements, choose the correct answer from the options given below:

A hydraulic automobile lift is designed to lift vehicles of mass $5000 \mathrm{~kg}$. The area of cross section of the cylinder carrying the load is $250 \mathrm{~cm}^{2}$. The maximum pressure the smaller piston would have to bear is $\left[\right.$ Assume $\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right]$

An air bubble of volume $1 \mathrm{~cm}^{3}$ rises from the bottom of a lake $40 \mathrm{~m}$ deep to the surface at a temperature of $12^{\circ} \mathrm{C}$. The atmospheric pressure is $1 \times 10^{5} \mathrm{~Pa}$ the density of water is $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$. There is no difference of the temperature of water at the depth of $40 \mathrm{~m}$ and on the surface. The volume of air bubble when it reaches the surface will be:

An aluminium rod with Young's modulus $Y=7.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ undergoes elastic strain of $0.04 \%$. The energy per unit volume stored in the rod in SI unit is:

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed.

Reason R: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.

In the light of the above statements, choose the most appropriate answer from the options given below

A small ball of mass $\mathrm{M}$ and density $\rho$ is dropped in a viscous liquid of density $\rho_{0}$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?

The Young's modulus of a steel wire of length $6 \mathrm{~m}$ and cross-sectional area $3 \mathrm{~mm}^{2}$, is $2 \times 10^{11}~\mathrm{N} / \mathrm{m}^{2}$. The wire is suspended from its support on a given planet. A block of mass $4 \mathrm{~kg}$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the earth. The elongation of wire is (Take $g$ on the earth $=10 \mathrm{~m} / \mathrm{s}^{2}$) :

A mercury drop of radius $10^{-3}~\mathrm{m}$ is broken into 125 equal size droplets. Surface tension of mercury is $0.45~\mathrm{Nm}^{-1}$. The gain in surface energy is :

If 1000 droplets of water of surface tension $0.07 \mathrm{~N} / \mathrm{m}$, having same radius $1 \mathrm{~mm}$ each, combine to from a single drop. In the process the released surface energy is :-

$\left( {\mathrm{Take}\,\pi = {{22} \over 7}} \right)$

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, $5 \mathrm{~cm}$. If the tube is dipped in a similar manner in another liquid $\mathrm{B}$ of surface tension and density double the values of liquid $\mathrm{A}$, the height of liquid column raised in liquid $\mathrm{B}$ would be __________ m.

Choose the correct relationship between Poisson ratio $(\sigma)$, bulk modulus (K) and modulus of rigidity $(\eta)$ of a given solid object :

A fully loaded boeing aircraft has a mass of $5.4\times10^5$ kg. Its total wing area is 500 m$^2$. It is in level flight with a speed of 1080 km/h. If the density of air $\rho$ is 1.2 kg m$^{-3}$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. ($\mathrm{g=10~m/s^2}$)

Surface tension of a soap bubble is $2.0 \times 10^{-2} \mathrm{Nm}^{-1}$. Work done to increase the radius of soap bubble from $3.5 \mathrm{~cm}$ to $7 \mathrm{~cm}$ will be:

Take $\left[\pi=\frac{22}{7}\right]$

A bicycle tyre is filled with air having pressure of $270 ~\mathrm{kPa}$ at $27^{\circ} \mathrm{C}$. The approximate pressure of the air in the tyre when the temperature increases to $36^{\circ} \mathrm{C}$ is

Match List I with List II

Choose the correct answer from the options given below :

A bowl filled with very hot soup cools from 98$^\circ$C to 86$^\circ$C in 2 minutes when the room temperature is 22$^\circ$C. How long it will take to cool from 75$^\circ$C to 69$^\circ$C?

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : Steel is used in the construction of buildings and bridges.

Reason R : Steel is more elastic and its elastic limit is high.

In the light of above statements, choose the most appropriate answer from the options given below

The frequency ($\nu$) of an oscillating liquid drop may depend upon radius ($r$) of the drop, density ($\rho$) of liquid and the surface tension (s) of the liquid as $\nu=r^a\rho^b s^c$. The values of a, b and c respectively are

A 100 m long wire having cross-sectional area $\mathrm{6.25\times10^{-4}~m^2}$ and Young's modulus is $\mathrm{10^{10}~Nm^{-2}}$ is subjected to a load of 250 N, then the elongation in the wire will be :

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): Clothes containing oil or grease stains cannot be cleaned by water wash.

Reason (R): Because the angle of contact between the oil/grease and water is obtuse.

In the light of the above statements, choose the correct answer from the option given below.

If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will :

A pressure-pump has a horizontal tube of cross sectional area $10 \mathrm{~cm}^{2}$ for the outflow of water at a speed of $20 \mathrm{~m} / \mathrm{s}$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is :

[given: density of water $=1000 \mathrm{~kg} / \mathrm{m}^{3}$]

Consider a cylindrical tank of radius $1 \mathrm{~m}$ is filled with water. The top surface of water is at $15 \mathrm{~m}$ from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of $5 \mathrm{~m}$ from the bottom. A force of $5 \times 10^{5} \mathrm{~N}$ is applied an the top surface of water using a piston. The speed of ifflux from the hole will be : (given atmospheric pressure $\mathrm{P}_{\mathrm{A}}=1.01 \times 10^{5} \mathrm{~Pa}$, density of water $\rho_{\mathrm{W}}=1000 \mathrm{~kg} / \mathrm{m}^{3}$ and gravitational acceleration $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )

A balloon has mass of $10 \mathrm{~g}$ in air. The air escapes from the balloon at a uniform rate with velocity $4.5 \mathrm{~cm} / \mathrm{s}$. If the balloon shrinks in $5 \mathrm{~s}$ completely. Then, the average force acting on that balloon will be (in dyne).

The force required to stretch a wire of cross-section $1 \mathrm{~cm}^{2}$ to double its length will be : (Given Yong's modulus of the wire $=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$)

A steel wire of length $3.2 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{s}}=2.0 \times 10^{11} \,\mathrm{Nm}^{-2}\right)$ and a copper wire of length $4.4 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{c}}=1.1 \times 10^{11} \,\mathrm{Nm}^{-2}\right)$, both of radius $1.4 \mathrm{~mm}$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4 \mathrm{~mm}$. The load applied, in Newton, will be: $\quad\left(\right.$ Given $\pi=\frac{22}{7}$)

Two cylindrical vessels of equal cross-sectional area $16 \mathrm{~cm}^{2}$ contain water upto heights $100 \mathrm{~cm}$ and $150 \mathrm{~cm}$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take, density of water $=10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2}$ ] :

The area of cross section of the rope used to lift a load by a crane is $2.5 \times 10^{-4} \mathrm{~m}^{2}$. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be :

(take $g=10 \,m s^{-2}$ )

A water drop of radius $1 \mathrm{~cm}$ is broken into 729 equal droplets. If surface tension of water is 75 dyne/ $\mathrm{cm}$, then the gain in surface energy upto first decimal place will be :

(Given $\pi=3.14$ )

A drop of liquid of density $\rho$ is floating half immersed in a liquid of density ${\sigma}$ and surface tension $7.5 \times 10^{-4}$ Ncm^$-$1. The radius of drop in $\mathrm{cm}$ will be :

(g = 10 ms^$-$2)

An air bubble of negligible weight having radius r rises steadily through a solution of density $\sigma$ at speed v. The coefficient of viscosity of the solution is given by :

A wire of length L is hanging from a fixed support. The length changes to L₁ and L₂ when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to :

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs^$-$1 and at a speed of 10 ms^$-$1. Then, the initial acceleration of the block, in ms^$-$2, will be :

A water drop of radius 1 $\mu$m falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 $\times$ 10^$-$5 Nsm^$-$2 and its density is negligible as compared to that of water 10⁶ gm^$-$3. Terminal velocity of the water drop is :

(Take acceleration due to gravity = 10 ms^$-$2)

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.

Reason R : Coefficient of viscosity = ${{Force} \over {Velocity\,gradient}}$

Choose the correct answer from the options given below :

A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be :

When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

The velocity of a small ball of mass 'm' and density d₁, when dropped in a container filled with glycerin, becomes constant after some time. If the density of glycerin is d₂, then the viscous force acting on the ball, will be :

If p is the density and $\eta$ is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number R_e is :

The terminal velocity (v_t) of the spherical rain drop depends on the radius (r) of the spherical rain drop as :

Potential energy as a function of r is given by $U = {A \over {{r^{10}}}} - {B \over {{r^5}}}$, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

The bulk modulus of a liquid is 3 $\times$ 10¹⁰ Nm^$-$2. The pressure required to reduce the volume of liquid by 2% is :