Practice Questions

Q9. A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity equals Y . When this rod is heated by temperature T and simultaneously subjected to a net longutudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to: (1) F/(3πr2Y T) (2) 9F/(πr2Y T) (3) 6F/(πr2Y T) (4) 3F/ (πr2Y T) Q10. 1 kg of water, at 20 °C is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of 20 Ω. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully is close to [ Specific heat of water = 4200 J kg−1 °C−1 Latent heat of water = 2260 kJ kg−1 ] (1) 3 min (2) 16 min (3) 22 min (4) 10 min

Q9. If 'M' is the mass of water that rises in a capillary tube of radius 'r' , then mass of water which will rise in a capillary tube of radius '2r' is: (1) 4 M (2) 2 M (3) M (4) M 2

Q9. A heavy ball of mass 𝑀 is suspended from the ceiling of a car by a light string of mass 𝑚 𝑚≪𝑀. When the car is at rest, the speed of transverse waves in the string is 60 ms-1 . When the car has acceleration 𝑎, the wave- speed increases to 60.5 ms-1 . The value of 𝑎, in terms of gravitational acceleration 𝑔, is closed to 𝑔 𝑔 (1) (2) 10 20 (3) 𝑔 (4) 𝑔 5 30

Q9. Two carnot engines A and B are operated in series. The first one, A, receives heat at T1(= 600K) and rejects to a reservoir at temperature T2. The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at T3(= 400K). Calculate the temperature T2 if the work outputs of the two engines are equal: (1) 500 K (2) 400 K (3) 300 K (4) 600 K

Q9. Half mole of an ideal monoatomic gas is heated at a constant pressure of 1 atm from 20° C to 90° C . Work done by the gas is (Gas constant, R = 8.21 J mol−1 K−1 ) (1) 73 J (2) 581 J (3) 291 J (4) 146 J

Q9. A wooden block floating in a bucket of water has 4 of its volume submerged. When certain amount of an oil is 5 poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is: (1) 0.8 (2) 0.7 (3) 0.5 (4) 0.6

Q9. Water flows into a large tank with flat bottom at the rate of 10−4 m3s−1. Water is also leaking out of a hole of area 1 cm2 at its bottom. If the height of the water in the tank remains steady then this height is: (1) 5.1 cm (2) 1.7 cm (3) 2.9 cm (4) 4 cm

Q9. The elastic limit of brass is 379 MPa. The minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit will be (1) 1.00 mm (2) 1.36 mm (3) 1.16 mm (4) 0.90 mm

Q9. When 𝑀1 gram of ice at -10oC (specific heat = 0.5 cal g-1 ℃-1 ) is added to 𝑀2 gram of water at 50 oC, finally no ice is left and the water is at 0 oC . The value of latent heat of ice, in cal g-1 is: (1) 50𝑀2 (2) 5𝑀1 - 50 𝑀1 𝑀2 5𝑀2 50𝑀2 (3) - 5 (4) - 5 𝑀1 𝑀1

Q9. A thermometer graduated according to a linear scale reads a value x0 when in contact with boiling water, and x0/3 when in contact with ice. What is the temperature of an object in ∘C , if this thermometer in the contact with the object reads x0/2? (1) 25 (2) 60 (3) 40 (4) 35

Q9. A cylinder with fixed capacity of 67.2 litre contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is: [Given that R = 8.31 J mol−1 K−1] (1) 748 J (2) 700 J (3) 350 J (4) 374 J

Q9. A rocket has to be launched from earth in such a way that it never returns. If 𝐸 is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have, if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon. E E (1) (2) 64 4 (3) E (4) E 32 16

Q9. Two satellites, A and B , have masses m and 2m respectively. A is in a circular orbit of radius R and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, KA is: KB (1) 2 (2) 21 (3) 1 (4) √12

Q10.A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is -180 J . The gas absorbs 250 J of heat along the path ab and 60 J along the path bc . The work done by the gas along the path abc is: (1) 130 J (2) 100 J (3) 120 J (4) 140 J JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper

Q10.A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is TVx = constant, then x is: (1) 3 (2) 2 5 5 (3) 2 (4) 5 3 3

Q10.Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of: (density of water = 100 kg / m3, coefficient of viscosity of water = 1 mPa s ) (1) 102 (2) 104 (3) 103 (4) 106

Q10.Young's moduli of two wires A and B are in the ratio 7: 4 . Wire A is 2 m long and has radius R . Wire B is 1.5 m long and has radius 2 mm . If the two wires stretch by the same length for a given load, the value of R is close to: (1) 1.3 mm (2) 1.9 mm (3) 1.5 mm (4) 1.7 mm

Q10.A rod, of length 𝐿 at room temperature and uniform area of cross section 𝐴, is made of a metal having coefficient of linear expansion 𝛼 / °𝐶 It is observed that an external compressive force 𝐹 is applied on each of its ends, prevents any change in the length of the rod when its temperature rises by ∆𝑇 K Young's modulus, 𝑌 for this metal is: 𝐹 2𝐹 (1) (2) 𝐴𝛼∆𝑇- 273 𝐴𝛼∆𝑇 𝐹 𝐹 (3) (4) 𝐴𝛼∆𝑇 2𝐴 𝛼∆𝑇 JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper

Q10.An unknown metal of mass 192 g heated to a temperature of 100°C was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4oC. Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5oC. ( Specific heat of brass is 394J kg−1K −1) (1) 916 J kg−1K −1 (2) 458 J kg−1K −1 (3) 654 J kg−1K −1 (4) 1232 J kg−1K −1 Q11. 2 kg of a monoatomic gas is at a pressure of 4 × 104 N m−2 . The density of the gas is 8 kg m−3 . What is the order of energy of the gas due to its thermal motion? (1) 105 J (2) 106 J (3) 104 J (4) 103 J JEE Main 2019 (10 Jan Shift 2) JEE Main Previous Year Paper

Q10.A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature, 27oC. The amount of heat transferred to the gas, so that R. M. S. velocity of molecules is doubled, is about. = 8 .3 J (K [R mole)−1] (1) 14 kJ (2) 10 kJ (3) 6 kJ (4) 0 .9 kJ

Q10.A heat source at T = 103 K is connected to another heat reservoir at T = 102 K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0 .1 W K−1 m−1 , the energy flux through it in the steady-state is: (1) 65 W m−2 (2) 120 W m−2 (3) 90 W m−2 (4) 200 W m−2

Q10.A 25 × 10−3 m3 volume cylinder is filled with 1 mol of O2 gas at room temperature (300 K) . The molecular diameter of O2 , and its root mean square speed, are found to be 0.3 nm and 200 m/s , respectively. What is the average collision rate (per second) for an O2 molecule? (1) ~1011 (2) ~1012 (3) ~1010 (4) ~1013

Q10.Two materials having coefficients of thermal conductivity 3K and K and thickness d and 3d respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are θ2 and θ1 respectively, (θ2 > θ1). The temperature at the interface is 5θ2 (1) θ2+θ1 (2) θ1 2 6 + 6 θ1 2θ2 θ1 9θ2 (3) 3 + 3 (4) 10 + 10

Q10.In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process the temperature of the gas is increased by ΔT . The amount of heat absorbed by gas is (R is gas constant): (1) 1 2 RΔT (2) 21 KRΔT (3) 2 3 RΔT (4) 2 3K ΔT

Q10.An ideal gas occupies a volume of 2 m3 at a pressure of 3 × 106 Pa. The energy of the gas is: (1) 108J (2) 9 × 106J (3) 3 × 102J (4) 6 × 104J