Practice Questions

Q6. A leak proof cylinder of length 1 m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0oC such that its height above the water surface is 20 cm. When the temperature of water is increased to 4oC, the height of the cylinder above the water surface becomes 21 cm. The density of water at T = 4oC, relative to the density at T = 0oC is close to: (1) 1.26 (2) 1.04 (3) 1.01 (4) 1.03

Q6. Two different wires having lengths L1 and L2 and respective temperature coefficient of linear expansion α1 and α2, are joined end-to-end. Then the effective temperature coefficient of linear expansion is : (1) α1L1+α2L2 (2) 2√α1α2 L1+L2 α1α2 L2L1 (3) α1+α2 (4) 4 2 α1+α2 (L2+L1)2

Q6. Water flows m a horizontal tube (see figure). The pressure of water changes by 700 Nm−2 between A and B where the area of cross section are 40 cm2 and 20 cm2, respectively. Find the rate of flow of water through the tube. (density of water = 1000 kgm−3 ) (1) 3020cm3/s (2) 2720cm3/s (3) 2420cm3/s (4) 1810cm3/s

Q6. A fluid is flowing through a horizontal pipe of varying cross-section, with v ms−1 at a point where the pressure is P Pascal. At another point where pressure P2 Pascal its speed is V ms−1 . If the density of the fluid is ρ kg −m−3 and the flow is streamline, then V is equal to + υ2 (1) √Pρ + υ (2) √2Pρ (3) √P2ρ + υ2 (4) √Pρ + υ2

Q6. A heat engine is involved with exchange of heat of 1915 J, –40 J, + 125 J and –Q J, during one cycle achieving and efficiency of 50. 0%. The value of Q is: (1) 640 J (2) 40 J (3) 980 J (4) 400 J

Q6. An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4cm and 4.8cm , respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is: (1) 9 (2) √3 16 2 (3) 3 (4) 81 4 256

Q6. A air bubble of radius 1 cm in water has an upward acceleration of 9.8 cms–2 . The density of water is 1 gm cm–3 and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980 cm/s2). JEE Main 2020 (04 Sep Shift 1) JEE Main Previous Year Paper (1) 4.51 gm (2) 3. 15 gm (3) 4.15 gm (4) 1.52 gm

Q6. Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm2 is 90 m s−1 . If the Young's modulus of wire is 16 × 1011 N m−2 , the extension of wire over its natural length is: (1) 0.03 mm (2) 0.02 mm (3) 0.04 mm (4) 0.01 mm

Q6. A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses m1 and m2(m1 > m2) are attached to the ends of the string. The system Is released from rest. The angular speed of the wheel when m1 descends by a JEE Main 2020 (09 Jan Shift 2) JEE Main Previous Year Paper distance h is: (1) 2(m1−m2)gh 21 (2) 2(m1+m2)gh 21 [ (m1+m2)R2+I ] [ (m1+m2)R2+I ] (3) (m1−m2) 21 (4) m1+m2 21 gh gh [ (m1+m2)R2+1 ] [ (m1+m2)R2+I ]

Q6. Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is: (1) 5 RT (2) 3 RT 2 2 (3) 9 RT (4) 3RT 2 JEE Main 2020 (03 Sep Shift 1) JEE Main Previous Year Paper

Q7. Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are vA and vB, respectively, then vA = n4 . The value of n is: vB (1) 4 (2) 1 (3) 2 (4) 3

Q7. Consider a solid sphere of radius R and mass density ρ(r) = ρ0(1 −r2R2 ), 0 < r ≤R. The minimum density of a liquid in which it will float is: (1) ρ0 (2) ρ0 3 5 (3) 2ρ0 (4) 2ρ0 5 3

Q7. Three rods of identical cross-section and length are made of three different materials of thermal conductivity K1, K2 and K3 , respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at 100°C and the other at 0°C (see figure). If the joints of the rod are at 70°C and JEE Main 2020 (06 Sep Shift 2) JEE Main Previous Year Paper 20°C in steady and there is no loss of energy from the surface of the rod, the correct relationship between K1, K2 and K3 is : (1) K1 : K3 = 2 : 3, (2) K1 < K2 < K3 K2 : K3 = 2 : 5 (3) K1 : K2 = 5 : 2, (4) K1 > K2 > K3 K1 : K3 = 3 : 5

Q7. Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently, the mean collision time between the gas molecule changes from τ1 to τ2 . If CPCv = γ for this gas then a good estimate for τ1τ2 is given by (1) 2 (2) 12 1 (3) ( 21 )γ (4) ( γ+1 2 ) 2

Q7. Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is off mass ′m′ and has another weight of mass 2 m hung at a distance of 75 cm from A . The tension in the string at A is: (1) 0. 5 mg (2) 2 mg (3) 0. 75 mg (4) 1 mg

Q7. A litre of dry air at STP expands adiabatically to a volume of 3 litres. If γ = 1.40, the work done by air is: (31.4 = 4.6555) [Take air to be an ideal gas] (1) 60.7J (2) 90.5J (3) 100.8J (4) 48J

Q7. A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is: JEE Main 2020 (04 Sep Shift 2) JEE Main Previous Year Paper (1) 1 (2) 2 √2 (3) 1 (4) √2

Q7. Molecules of an ideal gas are known to have three translational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of γ = ( CpCv ) are given, respectively, by (1) U = 52 RT and γ = 56 (2) U = 5 R T and γ = 57 (3) U = 25 RT and γ = 57 (4) U = 5RT and γ = 65

Q7. In an adiabatic process, the density of a diatomic gas becomes 32n times its initial value. The final pressure of the gas is found to be n times the initial pressure. The value of n is: JEE Main 2020 (05 Sep Shift 2) JEE Main Previous Year Paper (1) 32 (2) 326 (3) 128 (4) 321

Q7. A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wave train of wavelength 6 cm is produced at the lower and the rope. What is the wavelength of the wave train (in cm ) when it reaches the top of the rope? (1) 3 (2) 6 (3) 12 (4) 9

Q7. An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true ? (A) the mean free path of the molecules decreases (B) the mean collision time between the molecules decreases. (C) the mean free path remains unchanged. (D) the mean collision time relations unchanged. (1) (B) and (C) (2) (A)and (B) (3) (C) and (D) (4) (A) and (D) JEE Main 2020 (02 Sep Shift 2) JEE Main Previous Year Paper

Q7. Two liquids of densities ρ1 and ρ2(ρ2 = 2ρ1) are filled up behind a square wall of side 10m as shown in figure. Each liquid has a height of 5m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing): (1) 1 (2) 2 3 3 (3) 1 (4) 1 2 4

Q7. The specific heat of water = 4200 J kg–1 K–1 and the latent heat of ice = 3.4 × 105 J k g–1 . 100 grams of ice at 0 oC is placed in 200 g of water at 25 oC. The amount of ice that will melt as the temperature of water reaches 0 oC is close to (in grams) (1) 61.7 (2) 63. 8 (3) 69. 3 (4) 64. 6

Q7. A metallic sphere cools from 50 °C to 40 °C in 300 s. If atmospheric temperature around is 20 °C, then the sphere's temperature after the nest 5 minutes will be close to: (1) 31 °C (2) 33 °C (3) 28 °C (4) 35 °C

Q8. Two moles of an ideal gas, with CV CP = 35 , are mixed with three moles of another ideal gas CVCP = 34 . The value of CP for the mixture is CV (1) 1.45 (2) 1.50 (3) 1.47 (4) 1.42