Properties of Solids and Liquids — JEE Main PYQs

The surface tension of a soap bubble is $0.03 \text{ N/m}$. 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 $2000 \text{ kg/m}^3$ at a rate of $0.5 \text{ cm/s}$, then the coefficient of viscosity of liquid is ________ Poise. (Take $g = 10 \text{ m/s}^2$)

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

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

A string $A$ of length 0.314 m and Young's modulus $2 \times 10^{10} \text{ N/m}^2$ 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 $= 10 \text{ m/s}^2$)

(Mass of both strings is to be neglected as compared to the mass of load)

The surface tension of a soap solution is $3.5 \times 10^{-2}$ N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is $\alpha \times 10^{-6}$ J. The value of $\alpha$ is _______.

($\pi = 22/7$)

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 $2M$ 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 $(Y_A / Y_B)$ 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 $30 \text{ cm}^2$. The gun comprises of 10 perforations each of cross sectional area $15 \text{ mm}^2$. If the water flows in the hose with the speed of $50 \text{ cm/s}$, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

The temperature of a metal strip having coefficient of linear expansion $\alpha$ is increased from $T_1$ to $T_2$ resulting in increase of its length by $\Delta L_1$. The temperature is further increased from $T_2$ to $T_3$ such that the increase in its length is $\Delta L_2$.

Given $T_3 + T_1 = 2T_2$ and $T_2 - T_1 = \Delta T$, the value of $\Delta L_2$ is _______.

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 $12 \times 10^8 \text{ N/m}^2$. Area of cross-section of upper wire is $0.008 \text{ cm}^2$ and of lower wire is $0.004 \text{ cm}^2$. The maximum mass that can be added to pan without breaking any wire is ______ kg.

(take $g = 10 \text{ m/s}^2$)

[Figure: An upper wire hangs from the ceiling supporting a 30 kg block; a lower wire hangs from the 30 kg block supporting a 10 kg block; a pan hangs below the 10 kg block.]

A cube has side length 5 cm and modulus of rigidity $10^5 \text{ N/m}^2$. The displacement produced by a force of 10 N in the upper face of cube is _____ mm.

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).

A copper wire of length $3 \text{ m}$ is stretched by $3 \text{ mm}$ by applying an external force. The volume of the wire is $600 \times 10^{-6} \text{ m}^3$. The elastic potential energy stored in the wire in stretched condition would be __________ J.

(Given Young modulus of copper $= 1.1 \times 10^{11} \text{ N/m}^2$)

The heat extracted out of $x$ gram of water initially at $50\ °\text{C}$ to cool it down to $0\ °\text{C}$ is sufficient to evaporate $(1000 - x)$ gram of water also initially at $50\ °\text{C}$. The value of $x$ (closest integer) is ________.

(Take latent heat of water $2256 \text{ kJ/kg}$, specific heat capacity of water $4200 \text{ J/kg.K}$)

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

(take $g = 10\ \text{m/s}^2$ 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.

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 $10^{-5}$ m$^2$ then the Young's modulus of the wire is ________ N/m$^2$.

[Figure: Graph of $\Delta l\,(\times 10^{-4}\text{ m})$ on the y-axis (0 to 6) versus load $W$ (N) on the x-axis (0 to 60); a straight line through the origin passing through points such as (10, 1), (20, 2), ... (60, 6).]

A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is 528 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 liquid of density $600\,\text{kg/m}^3$ flowing steadily in a tube of varying cross-section. The cross-section at a point $A$ is $1.0\,\text{cm}^2$ and that at $B$ is $20\,\text{mm}^2$. Both the points $A$ and $B$ are in same horizontal plane, the speed of the liquid at $A$ is $10\,\text{cm/s}$. 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 ________.

A steel wire of length 2 m and Young's modulus $2.0\times10^{11}~\mathrm{N~m^{-2}}$ is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and $10^{-3}$ respectively, then the elastic potential energy density of the wire is _________ $\times10^{5}$ (in SI units).

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of $100~\mathrm{cm^2}$ with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density $1.5\times10^{3}~\mathrm{kg/m^3}$. What force one needs to apply on the hinged door so that it does not get opened ?

(Acceleration due to gravity $=10~\mathrm{m/s^2}$)

Match List - I with List - II.

	List - I		List - II
(A)	Heat capacity of body	(I)	$\mathrm{J\,kg^{-1}}$
(B)	Specific heat capacity of body	(II)	$\mathrm{J\,K^{-1}}$
(C)	Latent heat	(III)	$\mathrm{J\,kg^{-1}\,K^{-1}}$
(D)	Thermal conductivity	(IV)	$\mathrm{J\,m^{-1}\,K^{-1}\,s^{-1}}$

Choose the correct answer from the options given below :

Two water drops each of radius 'r' coalesce to form a bigger drop. If 'T' is the surface tension, the surface energy released in this process is :

The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N, the length of the string is 1.56 m. The original length of the string is _________ m.

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 cross-sectional 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:

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

Two cylindrical vessels of equal cross sectional area of $2\,\mathrm{m^2}$ contain water upto heights 10 m and 6 m, respectively. If the vessels are connected at their bottom then the work done by the force of gravity is (Density of water is $10^3\,\mathrm{kg/m^3}$ and $g = 10\,\mathrm{m/s^2}$)

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

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is $n$ times the volume of the bubble B, then, the value of $n$ is __________.

Consider a rectangular sheet of solid material of length $l = 9 \mathrm{~cm}$ and width $\mathrm{d} = 4 \mathrm{~cm}$. The coefficient of linear expansion is $\alpha = 3.1 \times 10^{-5} \mathrm{~K^{-1}}$ at room temperature and one atmospheric pressure. The mass of sheet $\mathrm{m} = 0.1 \mathrm{~kg}$ and the specific heat capacity $\mathrm{C_v} = 900 \mathrm{~J~kg^{-1}K^{-1}}$. If the amount of heat supplied to the material is $8.1 \times 10^{2} \mathrm{~J}$ then change in area of the rectangular sheet is :

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, $\mathrm{G} = 10^{10} \mathrm{~N/m^2}$)

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 wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is $1727°\mathrm{C}$ and power radiated by the wire is 94.2 W. Its emissivity is $\frac{x}{8}$ where $x =$ ____________.

(Given $\sigma = 6.0 \times 10^{-8}\ \mathrm{W\ m^{-2}\ K^{-4}}$, $\pi = 3.14$ and assume that the emissivity of wire material is same at all wavelength.)

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

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratios of lengths, radii and thermal conductivites of these rods are : $\dfrac{L_A}{L_B} = \dfrac{1}{2}$, $\dfrac{r_A}{r_B} = 2$ and $\dfrac{K_A}{K_B} = \dfrac{1}{2}$. The free ends of rods A and B are maintained at 400 K, 200 K, respectively. The temperature of rods interface is __________ K, when equilibrium is established.

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 $\mathrm{P} \times 10^{11}\ \mathrm{Nm}^{-2}$, where the value of P is: (Take $g = 3\pi\ \mathrm{m/s^2}$)

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool.

(Take $g = 10\ \mathrm{m/s^2}$, specific heat of water = 4200 J/(kg K))

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is 1 gm/cm$^3$.) The unknown mass is _____ kg.

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of 0.8 cm$^3$. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was __________ litre.

(Take 1 atm = $10^5$ Pa)

Two spherical bodies of the same material having radii $0.2\ \mathrm{m}$ and $0.8\ \mathrm{m}$ are kept in the same atmosphere. The temperature of the smaller body is $800\ \mathrm{K}$ and the temperature of the bigger body is $400\ \mathrm{K}$. If the energy radiated from the smaller body is E, the energy radiated from the bigger body is [neglect the effect of the temperature of the surroundings],

An amount of ice of mass $10^{-3}$ kg and temperature $-10°\mathrm{C}$ is transformed to vapour of temperature $110°\mathrm{C}$ by applying heat. The total amount of work required for this conversion is,

(Take, specific heat of ice $= 2100\ \mathrm{Jkg^{-1}K^{-1}}$, specific heat of water $= 4180\ \mathrm{Jkg^{-1}K^{-1}}$, specific heat of steam $= 1920\ \mathrm{Jkg^{-1}K^{-1}}$, Latent heat of ice $= 3.35 \times 10^5\ \mathrm{Jkg^{-1}}$ and Latent heat of steam $= 2.25 \times 10^6\ \mathrm{Jkg^{-1}}$)

Two soap bubbles of radius 2 cm and 4 cm, respectively, are in contact with each other. The radius of curvature of the common surface, in cm, is ________.

Three conductors of same length having thermal conductivity $k_1$, $k_2$ and $k_3$ are connected as shown in figure.

[Figure: conductors 1 ($k_1$) and 2 ($k_2$) side by side in parallel between the 100°C end and a common junction at temperature $\theta$°C; conductor 3 ($k_3$) connects the junction to the 0°C end]

Area of cross sections of $1^{st}$ and $2^{nd}$ conductor are same and for $3^{rd}$ conductor it is double of the $1^{st}$ conductor. The temperatures are given in the figure. In steady state condition, the value of $\theta$ is ________ °C.

(Given : $k_1 = 60\ \mathrm{Js^{-1}m^{-1}K^{-1}}$, $k_2 = 120\ \mathrm{Js^{-1}m^{-1}K^{-1}}$, $k_3 = 135\ \mathrm{Js^{-1}m^{-1}K^{-1}}$)

[Figure: a tapering tube; water enters the wider end marked (1) and leaves the narrower end marked (2)]

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 m/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)

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 $(5x_1 - 2x_2)$, 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

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension $0.095~\mathrm{J/m^2}$ and density $10^3~\mathrm{kg/m^3}$. The difference between pressure inside the bubble and atmospheric pressure is __________ $\mathrm{N/m^2}$.

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

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

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density $1000~\mathrm{kg/m^3}$. If the pressure inside the bubble is $2100~\mathrm{N/m^2}$ greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use $g = 10\,\mathrm{m/s^2}$)

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures ?

The temperature of a body in air falls from $40°\mathrm{C}$ to $24°\mathrm{C}$ in 4 minutes. The temperature of the air is $16°\mathrm{C}$. The temperature of the body in the next 4 minutes will be :

The increase in pressure required to decrease the volume of a water sample by 0.2% is $\mathrm{P} \times 10^5\ \mathrm{Nm}^{-2}$. Bulk modulus of water is $2.15 \times 10^9\ \mathrm{Nm}^{-2}$. The value of P is ______.

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:

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 $= 1000\,\mathrm{kg\,m^{-3}}$)

The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of $7 \times 10^6\,\mathrm{Pa}$, would be __________ $\mathrm{mm^3}$.

(Given bulk modulus of copper $= 1.4 \times 10^{11}\,\mathrm{N\,m^{-2}}$)

Given below are two statements :

Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $\mathrm{P_1 - P_2} = \rho g(\mathrm{h_2 - h_1})$.

Statement II : In ventury tube shown $2gh = v_1^2 - v_2^2$

[Figure: a venturi tube with a wide section (pressure $P_1$, area $A_1$, speed $v_1$) and a narrow section (pressure $P_2$, area $A_2$, speed $v_2$); two vertical tubes rise from the two sections with liquid level difference h]

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

On celcius scale the temperature of body increases by 40°C. The increase in temperature on Fahrenheit scale is :

A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/cm then the new radius is ________ cm. Take $\left(\pi = \frac{22}{7}\right)$.

An elastic spring under tension of 3 N has a length $a$. Its length is $b$ under tension 2 N. For its length $(3a - 2b)$, the value of tension will be ________ N.

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 :

Mercury is filled in a tube of radius 2 $cm$ up to a height of 30 $cm$. The force exerted by mercury on the bottom of the tube is ______ N.

(Given, atmospheric pressure $= 10^5~Nm^{-2}$, density of mercury $= 1.36 \times 10^4~kg\,m^{-3}$, $g = 10~m\,s^{-2}$, $\pi = \frac{22}{7}$)

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°.

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.

The density and breaking stress of a wire are $6 \times 10^4\ \mathrm{kg/m^3}$ and $1.2 \times 10^8\ \mathrm{N/m^2}$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}^{\text{rd}}$ of the value on the surface of earth. The maximum length of the wire with breaking is ________ m (take, $g = 10\ \mathrm{m/s^2}$).

Match List-I with List-II :

List-I	List-II
(A) A force that restores an elastic body of unit area to its original state	(I) Bulk modulus
(B) Two equal and opposite forces parallel to opposite faces	(II) Young's modulus
(C) Forces perpendicular everywhere to the surface per unit area same everywhere	(III) Stress
(D) Two equal and opposite forces perpendicular to opposite faces	(IV) Shear modulus

Choose the correct answer from the options given below :

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is ________ N.

[Figure: a U-shaped hydraulic press — the wider arm has diameter 14 cm; the thinner arm has diameter 1.4 cm with a 10 N force applied downward on it]

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 :

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $\frac{10}{x}$. The value of $x$ is _________.

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

A wire of cross sectional area A, modulus of elasticity $2 \times 10^{11}\ \mathrm{Nm^{-2}}$ and length 2 m is stretched between two vertical rigid supports. When a mass of 2 kg is suspended at the middle it sags lower from its original position making angle $\theta = \dfrac{1}{100}$ radian on the points of support. The value of A is ________ $\times 10^{-4}\ \mathrm{m^2}$ (consider $x \ll L$). (given : $g = 10\ \mathrm{m/s^2}$)

[Figure: wire of total span 2L fixed between two walls, midpoint sagging by x with angle θ at the supports, 2 kg mass hanging from the midpoint]

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

A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is $8 \times 10^{3}\ \mathrm{kg\ m^{-3}}$ and surface tension of soap solution is $0.28\ \mathrm{Nm^{-1}}$, then diameter of the soap bubble is________ cm. (if $g = 10\ \mathrm{m\ s^{-2}}$)

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) :

[Figure: a container with a layer of kerosene oil floating on water; an ice cube floats at the interface, partly in each liquid]

Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of 10 cm/s. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be ________ cm/s.

A sphere of relative density $\sigma$ and diameter D has concentric cavity of diameter d. The ratio of $\dfrac{D}{d}$, if it just floats on water in a tank is :

Two persons pull a wire towards themselves. Each person exerts a force of 200 N on the wire. Young's modulus of the material of wire is $1 \times 10^{11}\ \mathrm{N\,m^{-2}}$. Original length of the wire is 2 m and the area of cross section is $2\ \mathrm{cm^2}$. The wire will extend in length by ________ $\mu\mathrm{m}$.

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 $1\times10^{-4}$ m and density $10^5~\mathrm{kg/m^3}$ 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 $9.8\times10^{-6}~N~s/m^2$)

With rise in temperature, the Young's modulus of elasticity :

A plane is in level flight at constant speed and each of its two wings has an area of 40 $\mathrm{m^2}$. If the speed of the air is 180 km/h over the lower wing surface and 252 km/h over the upper wing surface, the mass of the plane is ________ kg. (Take air density to be 1 $\mathrm{kg\ m^{-3}}$ and $g = 10\ \mathrm{ms^{-2}}$)

A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :

One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be ________.

[Area of cross section of wire $= 0.005\ \mathrm{cm}^2$, $Y = 2 \times 10^{11}\ \mathrm{Nm}^{-2}$ and $g = 10\ \mathrm{ms}^{-2}$]

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 :

If average depth of an ocean is 4000 m and the bulk modulus of water is $2 \times 10^9\ \mathrm{Nm^{-2}}$, then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times 10^{-2}$. The value of $\alpha$ is ________. (Given, $g = 10\ \mathrm{ms^{-2}}$, $\rho = 1000\ \mathrm{kg\ m^{-3}}$)

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

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $70\ \mathrm{ms}^{-1}$ and $65\ \mathrm{ms}^{-1}$ respectively. If the wing area is $2\ \mathrm{m^2}$, the lift of the wing is _____ $N$.

(Given density of air $= 1.2\ \mathrm{kg\ m^{-3}}$)

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 :

Each of three blocks P, Q and R shown in figure has a mass of 3 kg. Each of the wires A and B has cross-sectional area $0.005~\mathrm{cm^2}$ and Young's modulus $2 \times 10^{11}~\mathrm{N~m^{-2}}$. Neglecting friction, the longitudinal strain on wire B is ________ $\times 10^{-4}$. (Take $\mathrm{g} = 10~\mathrm{m/s^2}$)

[Figure: blocks P and Q on a horizontal table connected by wire A; wire B runs from Q over a pulley at the table edge down to hanging block R]

A block of ice at $-10°C$ is slowly heated and converted to steam at $100°C$. Which of the following curves represent the phenomenon qualitatively:

A big drop is formed by coalescing $1000$ small identical drops of water. If $E_1$ be the total surface energy of $1000$ small drops of water and $E_2$ be the surface energy of single big drop of water, then $E_1 : E_2$ is $x : 1$ where $x =$ _______.

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?

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0.02% is _______ $m$.

(Take density of sea water $= 10^3\ \mathrm{kgm^{-3}}$, Bulk modulus of rubber $= 9 \times 10^8\ \mathrm{Nm^{-2}}$, and $g = 10\ \mathrm{ms^{-2}}$)

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 $2r$, falling through the same viscous medium will have terminal velocity:

Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $4.0 \times 10^{-5}$ m and Young's modulus of the metal is $2.0 \times 10^{11}$ N/m$^2$. The longitudinal strain developed in the wire is $\frac{1}{\alpha\pi}$. The value of $\alpha$ is ________. [Use $g = 10$ m/s$^2$]

[Figure: a smooth pulley fixed to the ceiling with a 2 kg block and a 4 kg block hanging from the two ends of the wire]