Title 6-properties-of-matter-.pdf ✅

Properties of Matter 1. A uniform rod rotating in gravity free region with certain constant angular velocity. The variation of tensile stress with distance x form axis of rotation is best represented by which of the following graphs: (A) (B) (C) (D) 2. Ice at 0 ∘C is to be 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 content is 40∘C. When a further 80 g of ice has been added and all it melted, the temperature of the whole content is 10∘C. Calculate the specific latent heat of fusion of ice. Take Sw = 1cal/gm∘C. (A) 3.8 × 105 J/kg (b) 1.2 × 105 J/kg(c) (C) 2.4 × 105 J/kg (d) 3.0 × 105 J/kg 3. The specific heat of a metal at low temperatures varies according to S = aT 3 where a is a constant and T is the absolute temperature. The heat energy needed to raise temperature of unit mass of the metal from T = 1K to T = 2K is: (A) 3a (B) 15a 4 (C) 2a 3 (D) 12a 5 4. 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% 5. A rod of length 2 m 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 6. 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) k1k2 k1+k2 (C) 1 4 (k1 + 3k2 ) (D) 1 4 (3k1 + k2 ) 7. 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 end 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 (A) (B) (C) (D) 8. A long solid cylinder is radiating power. It is remolded into a number of smaller cylinders, each of which has the same length as original cylinder. Each small cylinder has the same temperature as the original cylinder. The total radiant power emitted by the pieces is twice that emitted by the original cylinder. How many smaller cylinders are there? Neglect the energy emitted by the flat faces of cylinder. (A) 3 (B) 4 (C) 5 (D) 6 9. A black body calorimeter filled with hot water cools from 60∘C to 50∘C in 4 min and 40∘C to 30∘C in 8 min. The approximate temperature of surrounding is : (A) 10∘C (B) 15∘C (C) 20∘C (D) 25∘C 10. A uniform rod of mass m and length l is rotating with constant angular velocity ω about an axis which passes through its one end and perpendicular to the length of rod. The area of cross section of the rod is A and its Young's modulus is Y (neglect gravity). The strain at the mid point of the rod is : (A) mω2l 8AY (B) 3mω2l 8AY
(C) 3mω2l 4AY (D) mω2l 4AY 11. A steel wire with cross section 3 cm2 has elastic limit 2.4 × 108 pa. The maximum upward acceleration that can be given to 1200 kg elevator supported by this cable if the stress is not to exceed 1/3 rd of the elastic limit is : (g = 10 m/s 2 ) (A) 9 ms−2 (B) 10 ms−2 (C) 11 ms−2 (D) 12 ms−2 12. Two metallic spheres S1 and S2 are made of the same material and have got identical surface finish. The mass of S1 is thrice that of S2. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of S1 to that of S2 is: (A) 1 3 (B) 1 √3 (C) √3 1 (D) ( 1 3 ) 1/3 13. A clock with an iron pendulum and periodic time 1sec keeps correct time at 10∘C. The error in seconds per day if the temperature is 20∘C is : (Take α = 10 × 10−6 / ∘C ) (A) 4.32sec (B) 8.64sec (C) 2sec (D) 1sec 14. The temperature of a well stirred liquid kept open to a cold surrounding is plotted against time. The value of sec2 θ1 is: (A) 1 + 9tan2 θ2 (B) 1 + tan2 θ2 (C) 1 + 3tan2 θ2 (D) 3 + tan2 θ2 15. Select the correct statement on the basis of the given graph : (A) Young's modulus of A is greater but it is less ductile (B) Young's modulus of A is greater and it is more ductile (C) Young's modulus of A is less and it is less ductile (D) Young's modulus of A is less but it is more ductile MULTIPLE CORRECT ANSWERS TYPEEach of the following Question has 4 choices A, B, C & D, out of which ONE or MORE Choices may be Correct: 16. Which of the following are correct? (A) The bulk modulus of an incompressible liquid is infinity. (B) Bulk modulus of a perfectly rigid body is infinity. (C) According to Hooke's law, the ratio of the stress and strain remains constant. (D) None of the above 17. The water equivalent of a copper calorimeter is 4.5 g. If the specific heat of copper is 0.09cal/g/ ∘C (A) mass of the calorimeter is 0.5 kg (B) thermal capacity of the calorimeter is 4.5cal/ ∘C (C) heat required to raise the temperature of the calorimeter by 8 ∘C will be 36cal (D) heat required to melt 15 g of ice at 0 ∘C placed in the calorimeter will be 1200cal 18. A composite rod consists of a steel rod of length 25 cm and area 2A and a copper rod of length 50 cm and area A are joined end to end. The composite rod is subjected to an axial load F. If the Young's modulus of steel and copper are in the ratio 2: 1, then: (A) The extension produced in copper rod will be more. (B) The extension in copper and steel parts will be in the ratio 2: 1. (C) The stress in the copper rod will be more. (D) No extension will be produced. 19. Four rods A, B, C,D of same length and material but of different radii r, r√2, r√3, and 2r respectively are held between two rigid walls. The temperature of all rods is increased by same amount. If the rods do not bend, then
(A) The stress in the rods are in the ratio 1: 2: 3: 4. (B) The force on the rod exerted by the wall are in the ratio 1: 2: 3: 4. (C) The energy stored in the rods due to elasticity are in the ratio 1: 2: 3: 4. (D) The strains produced in the rods are in the ratio 1: 2: 3: 4. 20. Heat is supplied to a certain homogenous sample of matter, at a uniform rate. Its temperature is plotted against time, as shown. Which of the following conclusions can be drawn? (A) Its specific heat capacity is greater in the solid state than in the liquid state (B) Its specific heat capacity is greater in the liquid state than in the solid state (C) Its latent heat of vaporization is greater than its latent heat of fusion (D) Its latent heat of vaporization is smaller than its latent heat of fusion 21. One end of a conducting rod is maintained at temperature 50∘C and at other end, ice is melting at 0 ∘C. The rate of melting of ice is doubled if : (A) The temperature is made 200∘C and the area of cross-section of the rod is halved (B) The temperature is made 100∘C and length of rod is made four times (C) Area of cross-section of rod is halved and length is doubled (D) The temperature is made 100∘C and the area of cross-section of rod and length both are doubled. 22. Two metallic spheres A and B are made of same material and have got identical surface finish. The mass of sphere A is four time that of B. Both the sphere are heated to the same temperature and placed in a room having lower temperature but thermally insulated from each other. (A) The ratio of rate of heat loss of A to that of B is 2 4/3 . (B) The ratio of rate of heat loss of A to that of B is 2 2/3 . (C) The ratio of the initial rate of cooling of A to that of B is 2 −2/3 (D) The ratio of the initial rate of cooling of A to that of B is 2 −4/3 . 23. Iron floats over mercury because density of mercury is more than the density of iron. Coefficient of volumetric expansion of iron and mercury are 35 × 10−6 ∘C −1 and 180 × 10−6 ∘C −1 . Now consider an iron cube floating in a bowl of mercury at 0 ∘C. When temperature is increased upto 25∘C, then choose the correct options. (A) Cube is submerged more at 25∘C (B) Cube is submerged less at 25∘C (C) Percentage change in the fraction of volume submerged is about 1% (D) Percentage change in the fraction of volume submerged is about 0.4% 24. A sample A of liquid water and a sample B of ice of identical mass are kept in two neighbouring chambers in an otherwise insulated container. The chambers can exchange heat with each other. The graph of temperatures of the two chambers is plotted with time. Sice = Swater 2 . (A) Finally the contents in sample A is water (B) Equilibrium temperature is freezing point of water (C) Ice melts partly (D) Finally the contents in sample B is ice only 25. Two surfaces of same nature and area but of different material are heated to same temperature. They are allowed to cool down in same surroundings. If dQ dt represents rate of loss of heat and dθ dt represents rate of fall of temperature, then initially for both : (A) dQ dt is same (B) dQ dt is different (C) dθ dt is same (D) dθ dt is diferent 26. Four identical rods which have thermally insulated lateral surfaces are joined at point A. Points B, C,D and E are connected to large reservoirs. If heat flows into the junction from point B at rate of 1W