PHYSICS
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Quest
QUESTION FOR SHORT ANSWER
Q.1 Can one object be hotter than another if they are at the same temperature? Explain.
Q.2 What qualities make a particular thermometric property suitable for use in a practical thermometer? Q.3 You put two uncovered pails of water, one containing hot water and one containing cold water, outside
in below-freezing weather. The pail with the hot water will usually begin to freeze first.Why? What would happen if you covered the pails?
Q.4 Can a temperature be assigned to a vacuum?
Q.5 What are the dimensions of α, the coefficient of linear expansion? Does the value of α depend on the unit of length used? When Fahrenheit degrees are used instead of Celsius degrees as the unit of temperature change, does the numerical value of α change? If so, how? If not, prove it.
Q.6 A metal ball can pass through a metal ring. When the ball is heated, however, it gets stuck in the ring. What would happen if the ring, rather than the ball, were heated?
Q.7 Two strips, one of iron and one of zinc, are riveted together side by side to form a straight bar that curves when heated. Why is the iron on the inside of the curve?
Q.8 Explain how the period of a pendulum clock can be kept constant with temperature by attaching vertical tubes of mercury to the bottom of the pendulum.
Q.9 What causes water pipes to burst in the winter?
Q.10 Do the pressure and volume of air in a house change when the furnace raises the temperature significantly? If not, is the ideal gas law violated?
Q.11 If two systems are in thermal equilibrium, they have the same temperature. Is the converse true? That is, if two systems have the same temperature, are they in thermal equilibrium? What can you say about two systems that have different temperatures?
Q.12 As a practical matter, there is always a temperature difference between a system and some part of its environment, however remote. Must there always be some heat transferred because of that temperature difference? Explain.
Quest
ONLY ONE OPTION IS CORRECT. Take approx. 2 minutes for answering each question.
Q.1 Overall changes in volume and radii of a uniform cylindrical steel wire are 0.2% and 0.002% respectively when subjected to some suitable force. Longitudinal tensile stress acting on the wire is
(Y = 2.0 × 1011 Nm–2)
(A) 3.2 × 109 Nm–2 (B) 3.2 × 107 Nm–2 (C) 3.6 × 109 Nm–2
(D) 3.6 × 107 Nm–2 (E) 4.08 × 103 Nm–3
Q.2 A solid sphere of radius R made of of material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. When a mass m is placed on the piston to compress the liquid, the fractional change in the radius of the sphere δR/R is
(A) mg/AK (B) mg/3AK (C) mg/A (D) mg/3AR
Q.3 A cylindrical wire of radius 1 mm, length 1 m, Young’s modulus = 2 × 1011 N/m2, poisson’s ratio
µ = π/10 is stretched by a force of 100 N. Its radius will become
(A) 0.99998 mm (B) 0.99999 mm (C) 0.99997 mm (D) 0.99995 mm
Q.4 A uniform rod rotating in gravity free region with certain constant angular velocity. The variation of tensile stress with distance x from axis of rotation is best represented by which of the following graphs.
(A) (B) (C) (D)
Q.5 A metallic wire of length L is fixed between two rigid supports. If the wire is cooled through a temperature difference ∆T (Y = young’s modulus, ρ = density, α = coefficient of linear expansion) then the frequency of transverse vibration is proportional to :
(A) Y ρ α (B) ρ α Y (C) α ρ Y (D) Y ρα
Q.6 A metal wire is clamped between two vertical walls. At 20 °C the unstrained length of the wire is exactly equal to the separation between walls. If the temperature of the wire is decreased the graph between elastic energy density (u) and temperature (T) of the wire is
(A) (B) (C) (D)
Q.7 A rod of length 2m rests on smooth horizontal floor. If the rod is heated from 0°C to 20°C. Find the longitudinal strain developed? (α = 5 × 10–5/°C)
(A) 10–3 (B) 2 × 10–3 (C) Zero (D) None
Q.8 The load versus strain graph for four wires of the same material is shown in the figure. The thickest wire is represented by the line
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Q.9 A steel tape gives correct measurement at 20°C. A piece of wood is being measured with the steel tape at 0°C. The reading is 25 cm on the tape, the real length of the given piece of wood must be:
(A) 25 cm (B) <25 cm (C) >25 cm (D) can not say
Q.10 A rod of length 20 cm is made of metal. It expands by 0.075 cm when its temperature is raised from 0°C to 100°C. Another rod of a different metal B having the same length expands by 0.045 cm for the same change in temperature, a third rod of the same length is composed of two parts one of metal A and the other of metal B. Thus rod expand by 0.06 cm.for the same change in temperature. The portion made of metal A has the length :
(A) 20 cm (B) 10 cm (C) 15 cm (D) 18 cm
Q.11 A sphere of diameter 7 cm and mass 266.5 gm floats in a bath of a liquid. As the temperature is raised, the sphere just begins to sink at a temperature 35°C. If the density of a liquid at 0°C is 1.527 gm/cc, then neglecting the expansion of the sphere, the coefficient of cubical expansion of the liquid is f :
(A) 8.486 × 10−4 per 0C (B) 8.486 × 10−5 per 0C
(C) 8.486 × 10−6 per 0C (D) 8.486 × 10−3 per 0C
Q.12 The volume of the bulb of a mercury thermometer at 0°C is V0 and cross section of the capillary is A0. The coefficient of linear expansion of glass is ag per °C and the cubical expansion of mercury γm per °C. If the mercury just fills the bulb at 0°C, what is the length of mercury column in capillary at T°C. (A)
(
)
(
1 2 T)
A 3 T V g 0 g m 0 a a + + γ (B)(
)
(
1 2 T)
A 3 T V g g m a a 0 0 + − γ (C)(
)
(
1 3 T)
A 2 T V g g m a a 0 0 + + γ (D)(
)
(
1 3 T)
A 2 T V g g m a a 0 0 + − γQ.13 A metallic rod l cm long with a square cross-section is heated through 1°C. If Young’s modulus of elasticity of the metal is E and the mean coefficient of linear expansion is α per degree Celsius, then the compressional force required to prevent the rod from expanding along its length is :(Neglect the change of cross-sectional area)
(A) EAαt (B) EAαt/(1 + αt) (C) EAαt/(1−αt) (D) E/αt
Q.14 The loss in weight of a solid when immersed in a liquid at 0°C is W0 and at t°C is W. If cubical coefficient of expansion of the solid and the liquid by γS and γ 1 respectively, then W is equal to :
(A) W0 [1 + ( γs – γl) t] (B) W0 [1 - (γs – γl)t] (C) W0 [(γ s – γl) t] (D) W0t/(γs – γl)
Q.15 A thin walled cylindrical metal vessel of linear coefficient of expansion 10–3 °C–1 contains benzenr of
volume expansion coefficient 10–3°C–1. If the vessel and its contents are now heated by 10°C, the
pressure due to the liquid at the bottom.
(A) increases by 2% (B) decreases by 1% (C) decreases by 2% (D) remains unchanged Q.16 A rod of length 2m at 0°C and having expansion coefficient α = (3x + 2) × 10–6 °C–1 where x is the
distance (in cm) from one end of rod. The length of rod at 20°C is :
(A) 2.124 m (B) 3.24 m (C) 2.0120 m (D) 3.124 m
Q.17 A copper ring has a diameter of exactly 25 mm at its temperature of 0°C. An aluminium sphere has a diameter of exactly 25.05 mm at its temperature of 100°C. The sphere is placed on top of the ring and two are allowed to come to thermal equilibrium, no heat being lost to the surrounding. The sphere just passes through the ring at the equilibrium temperature. The ratio of the mass of the sphere & ring is : (given : αCu = 17 × 10–6 /°C, α
Al = 2.3 × 10
–5 /°C, specific heat of Cu = 0.0923 Cal/g°C and specific
heat of Al = 0.215 cal/g°C)
Quest
Q.18 A cuboid ABCDEFGH is anisotropic with αx = 1 × 10–5 /°C,
αy = 2 × 10–5 /°C, α
z = 3 × 10–5 /°C. Coefficient of superficial
expansion of faces can be
(A) βABCD = 5 × 10–5 /°C (B) β
BCGH = 4 × 10
–5 /°C
(C) βCDEH = 3 × 10–5 /°C (D) β
EFGH = 2 × 10–5 /°C
Q.19 An open vessel is filled completely with oil which has same coefficient of volume expansion as that of the vessel. On heating both oil and vessel,
(A) the vessel can contain more volume and more mass of oil (B) the vessel can contain same volume and same mass of oil (C) the vessel can contain same volume but more mass of oil (D) the vessel can contain more volume but same mass of oil
Q.20 A metal ball immersed in Alcohol weights W1 at 0°C and W2 at 50°C. The coefficient of cubical expansion of the metal (γ)m is less than that of alcohol (γ)Al. Assuming that density of metal is large compared to that of alcohol, it can be shown that
(A) W1 > W2 (B) W1 = W2 (C) W1 < W2 (D) any of (A) , (B) or (C) Q.21 A solid ball is completely immersed in a liquid. The coefficients of volume expansion of the ball and liquid
are 3 × 10–6 and 8 × 10–6 per °C respectively. The percentage change in upthrust when the temperature
is increased by 100 °C is
(A) 0.5 % (B) 0.11 % (C) 1.1 % (D) 0.05 %
Q.22 A thin copper wire of length L increase in length by 1% when heated from temperature T1 to T2. What is the percentage change in area when a thin copper plate having dimensions 2L × L is heated from T1 to T2?
(A) 1% (B) 2% (C) 3% (D) 4%
Q.23 If two rods of length L and 2L having coefficients of linear expansion α and 2α respectively are connected so that total length becomes 3L, the average coefficient of linear expansion of the composition rod equals: (A) 2 3 α (B) 2 5 α (C) 3 5 α (D) none of these
Q.24 The bulk modulus of copper is 1.4 × 1011 Pa and the coefficient of linear expansion is 1.7 × 10–5 (C°)–1. What hydrostatic pressure is necessary to prevent a copper block from expanding
when its temperature is increased from 20°C to 30°C?
(A) 6.0 × 105 Pa (B) 7.1 × 107 Pa (C) 5.2 × 106 Pa (D) 40 atm
Q.25 The coefficients of thermal expansion of steel and a metal X are respectively 12 × 10–6 and 2 × 10–6 per°C. At 40°C, the side of a cube of metal X was measured using a steel vernier callipers. The
reading was 100 mm. Assuming that the calibration of the vernier was done at 0°C, then the actual length of the side of the cube at 0°C will be
(A) > 100 mm (B) < 100 mm (C) = 100 mm (D) data insufficient to conclude Q.26 A glass flask contains some mercury at room temperature. It is found that at different temperatures the volume of air inside the flask remains the same. If the volume of mercury in the flask is 300 cm3, then volume of the flask is (given that coefficient of volume expansion of mercury and coefficient of linear expansion of glass are 1.8 × 10–4 (°C)–1 and 9 × 10–6 (°C)–1 respectively)
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Question No. 27 to 31 (5 question)
Solids and liquids both expand on heating. The density of substance decreases on expanding according to the relation ) T T ( 1 2 1 1 2 +γ − ρ = ρ where, ρ1 —→ density at T1 ρ2 —→ density at T2
γ —→ coeff. of volume expansion of substances
when a solid is submerged in a liquid, liquid exerts an upward force on solid which is equal to the weight of liquid displaced by submerged part of solid.
Solid will float or sink depends on relative densities of solid and liquid.
A cubical block of solid floats in a liquid with half of its volume submerged in liquid as shown in figure (at temperature T)
αS —→ coeff. of linear expansion of solid γL —→ coeff. of volume expansion of liquid
ρS —→ density of solid at temp. T ρL —→ density of liquid at temp. T Q.27 The relation between densities of solid and liquid at temperature T is
(A) ρS = 2ρL (B) ρS = (1/2)ρL (C) ρS = ρL (D) ρS = (1/4)ρL Q.28 If temperature of system increases, then fraction of solid submerged in liquid
(A) increases (B) decreases (C) remains the same (D) inadequate information Q.29 Imagine fraction submerged does not change on increasing temperature the relation between γL and αS is
(A) γL = 3αS (B) γL = 2αS (C) γL = 4αS (D) γL = (3/2)αS
Q.30 Imagine the depth of the block submerged in the liquid does not change on increasing temperature then (A) γL = 2α (B) γL = 3α (C) γL = (3/2)α (D) γL = (4/3)α
Q.31 Assume block does not expand on heating. The temperature at which the block just begins to sink in liquid is
(A) T + 1/γL (B) T + 1/(2γL) (C) T + 2/γL (D) T + γL/2
Q.32 The coefficient of apparent expansion of a liquid in a copper vessel is C and in a silver vessel is S. The coefficient of volume expansion of copper is γc. What is the coefficient of linear expansion of silver? (A) (C+γc+S) 3 (B) (C−γc+S) 3 (C) (C+γc−S) 3 (D) (C−γc−S) 3
Q.33 An aluminium container of mass 100 gm contains 200 gm of ice at – 20°C. Heat is added to the system at the rate of 100 cal/s. The temperature of the system after 4 minutes will be (specific heat of ice = 0.5 and L = 80 cal/gm, specific heat of Al = 0.2 cal/gm/°C)
Quest
Q.34 A thermally insulated vessel contains some water at 00C. The vessel is connected to a vacuum pump to
pump out water vapour. This results in some water getting frozen. It is given Latent heat of vaporization of water at 0°C =21 × 105 J/kg and latent heat of freezing of water = 3.36 × 105 J/kg. The maximum
percentage amount of water that will be solidified in this manner will be
(A) 86.2% (B) 33.6% (C) 21% (D) 24.36%
Q.35 A block of mass 2.5 kg is heated to temperature of 500°C and placed on a large ice block. What is the maximum amount of ice that can melt (approx.). Specific heat for the body = 0.1 Cal/gm°C.
(A) 1 kg (B) 1.5 kg (C) 2 kg (D) 2.5 kg
Q.36 10 gm of ice at 0°C is kept in a calorimeter of water equivalent 10 gm. How much heat should be supplied to the apparatus to evaporate the water thus formed? (Neglect loss of heat)
(A) 6200 cal (B) 7200 cal (C) 13600 cal (D) 8200 cal
Q.37 Heat is being supplied at a constant rate to a sphere of ice which is melting at the rate of 0.1 gm/sec. It melts completely in 100 sec. The rate of rise of temperature thereafter will be
(Assume no loss of heat.)
(A) 0.8 °C/sec (B) 5.4 °C/sec (C) 3.6 °C/sec (D) will change with time Q.38 1 kg of ice at – 10°C is mixed with 4.4 kg of water at 30°C. The final temperature of mixture is :
(specific heat of ice is 2100 J/kg/k)
(A) 2.3°C (B) 4.4°C (C) 5.3°C (D) 8.7°C
Q.39 Steam at 100°C is added slowly to 1400 gm of water at 16°C until the temperature of water is raised to 80°C. The mass of steam required to do this is (LV = 540 cal/gm) :
(A) 160 gm (B) 125 mg (C) 250 gm (D) 320 gm
Q.40 A 2100 W continuous flow geyser (instant geyser) has water inlet temperature = 10°C while the water flows out at the rate of 20 g/sec. The outlet temperature of water must be about
(A) 20°C (B) 30°C (C) 35°C (D) 40°C
Q.41 A continuous flow water heater (geyser) has an electrical power rating = 2 kW and efficienty of conversion of electrical power into heat = 80%. If water is flowing through the device at the rate of 100 cc/sec, and the inlet temperature is 10°C, the outlet temperature will be
(A) 12.2°C (B) 13.8°C (C) 20°C (D) 16.5°C
Q.42 Ice at 0°C is added to 200 g of water initially at 70°C in a vacuum flask. When 50 g of ice has been added and has all melted the temperature of the flask and contents is 40°C. When a further 80g of ice has been added and has all metled, the temperature of the whole is 10°C. Calculate the specific latent heat of fusion of ice.[Take Sw =1 cal /gm °C.]
(A) 3.8 ×105 J/ kg (B) 1.2 ×105 J/ kg (C) 2.4 ×105 J/ kg (D) 3.0 ×105 J/ kg
Q.43 A solid material is supplied with heat at a constant rate. The temperature of material is changing with heat input as shown in the figure. What does slope DE represent.
(A) latent heat of liquid (B) latent heat of vapour (C) heat capacity of vapour
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Q.44 Two vertical glass tubes filled with a liquid are connected by a capillary tube as shown in the figure. The tube on the left is put in an ice bath at 0°C while the tube on the right is kept at 30°C in a water bath. The difference in the levels of the liquid in the two tubes is 4 cm while the height of the liquid column at 0°C is 120 cm. The coefficient of volume expansion of liquid is (Ignore expansion of glass tube)
(A) 22 × 10–4/°C (B) 1.1 × 10–4/°C
(C) 11 × 10–4/°C (D) 2.2 × 10–4/°C
Q.45 A system S receives heat continuously from an electrical heater of power 10W. The temperature of S becomes constant at 50°C when the surrounding temperature is 20°C. After the heater is switched off, S cools from 35.1°C to 34.9°C in 1 minute. The heat capacity of S is
(A) 100J/°C (B) 300J/°C (C) 750J/°C (D) 1500J/°C
Q.46 A block of ice with mass m falls into a lake. After impact, a mass of ice m/5 melts. Both the block of ice and the lake have a temperature of 0°C. If L represents the heat of fusion, the minimum distance the ice fell before striking the surface is
(A) g 5 L (B) g L 5 (C) m 5 gL (D) g 5 mL
Q.47 Pure water super cooled to −15°C is contained in a thermally insulated flask. Small amount of ice is thrown into the flask. The fraction of water frozen into ice is :
(A) 3/35 (B) 6/35 (C) 6/29 (D) 2/35
Q.48 The specific heat of a metal at low temperatures varies according to S = aT3 where a is a constant and
T is the absolute temperature. The heat energy needed to raise unit mass of the metal from T = 1 K to T = 2 K is (A) 3 a (B) 4 a 15 (C) 3 a 2 (D) 5 a 12
Q.49 The graph shown in the figure represent change in the temperature of 5 kg of a substance as it abosrbs heat at a constant rate of 42 kJ min–1.
The latent heat of vapourazation of the substance is : (A) 630 kJ kg–1
(B) 126 kJ kg–1
(C) 84 kJ kg–1
(D) 12.6 kJ kg–1
Q.50 The density of a material A is 1500 kg/m3 and that of another material B is 2000 kg/m3. It is found that the heat capacity of 8 volumes of A is equal to heat capacity of 12 volumes of B. The ratio of specific heats of A and B will be
(A) 1 : 2 (B) 3 : 1 (C) 3 : 2 (D) 2 : 1
Q.51 Find the amount of heat supplied to decrease the volume of an ice water mixture by 1 cm3 without any
change in temperature. (ρice = 0.9 ρwater, Lice = 80 cal/gm).
Quest
Q.52 Some steam at 100°C is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02 kg at 15°C so that the temperature of the calorimeter and its contents rises to 80°C. What is the mass of steam condensing. (in kg)
(A) 0.130 (B) 0.065 (C) 0.260 (D) 0.135
Q.53 One end of a 2.35m long and 2.0cm radius aluminium rod (K = 235 W.m−1K−1) is held at 200C. The other
end of the rod is in contact with a block of ice at its melting point. The rate in kg.s−1 at which ice melts is
(A) 48π × 10−6 (B) 24π × 10−6 (C) 2.4π × 10−6 (D) 4.8π × 10−6
[Take latent heat of fusion for ice as 3 10
×105 J.kg−1]
Q.54 Four rods of same material with different radii r and length l are used to connect two reservoirs of heat at different temperatures. Which one will conduct most heat ?
(A) r =2cm, l =0.5m (B) r = 2cm, l = 2m (C) r =0.5cm, l =0.5m (D) r = 1 cm, l = 1 m
Q.55 A cylinder of radius R made of a material of thermal conductivity k1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity k2. The two ends of the combined system are maintained at different temperatures. There is no loss of heat from the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is
(A) k1 + k2 (B) 2 1 2 1 k k k k + (C) 1 4(k1 + 3k2) (D) 1 4(3k + k2)
Q.56 Heat is conducted across a composite block of two slabs of thickness d and 2d. Their thermal conductivities are 2k and k respectively. All the heat entering the face AB leaves from the face CD. The temperature in °C of the junction EF of the two slabs is :
(A) 20 (B) 50 (C) 60 (D)80 A B E F C D
Q.57 A sphere of ice at 0°C having initial radius R is placed in an environment having ambient temperature > 0°C. The ice melts uniformly, such that shape remains spherical. After a time ‘t’ the radius of the sphere has reduced to r. Assuming the rate of heat absorption is proportional to the surface area of the sphere at any moment, which graph best depicts r (t).
(A) (B) (C) (D)
Q.58 A rod of length L and uniform cross-sectional area has varying thermal conductivity which changes linearly from 2K at end A to K at the other end B. The ends A and B of the rod are maintained at constant temperature 100°C and 0°C, respectively. At steady state, the graph of temperature : T = T(x) where x = distance from end A will be
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Q.59 Two sheets of thickness d and 2 d and same area are touching each other on their face. Temperature TA, TB, TC shown are in geometric progression with common ratio r = 2. Then ratio of thermal conductivity of thinner and thicker sheet are
(A) 1 (B) 2 (C) 3 (D) 4
Q.60 The wall with a cavity consists of two layers of brick separated by a layer of air. All three layers have the same thickness and the thermal conductivity of the brick is much greater than that of air. The left layer is at a higher temperature than the right layer and steady state condition exists. Which of the following graphs predicts correctly the variation of temperature T with distance d inside the cavity?
(A) (B) (C) (D)
Q.61 A wall has two layer A and B each made of different material, both the layers have the same thickness. The thermal conductivity of the material A is twice that of B. Under thermal equilibrium the temperature difference across the wall B is 36°C. The temperature difference across the wall A is
(A) 6°C (B) 12°C (C) 18°C (D) 72°C
Q.62 A ring consisting of two parts ADB and ACB of same conductivity k carries an amount of heat H. The ADB part is now replaced with another metal keeping the temperatures T1 and T2 constant. The heat carried increases to 2H. What should be the conductivity of the new ADB part? Given
ADB ACB = 3: (A) 3 7 k (B) 2 k (C) 2 5 k (D) 3 k
Q.63 Three conducting rods of same material and cross-section are shown in figure. Temperatures of A, D and C are maintained at 20°C, 90°C and 0°C. The ratio of lengths of BD and BC if there is no heat flow in AB is:
(A) 2 / 7 (B) 7 / 2 (C) 9 / 2 (D) 2 / 9
Q.64 Three rods made of the same material and having same cross-sectional area but different lengths 10cm, 20 cm and 30 cm are joined as shown. The temperature of the joint is: