Practice Questions

Q7. Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is 24 π × 102 N m−2 . What is the minimum radius of the wire ? ( take g = 10 m s−2) (1) 1250 cm (2) 1. 25 cm (3) 125 cm (4) 12. 5 cm

Q7. Consider a planet in some solar system that has a mass double the mass of earth and density equal to the average density of the earth. If the weight of an object on earth is W , the weight of the same object on that planet will be: (1) 2W (2) W (3) 2 13 W (4) √2 W

Q7. Two identical metal wires of thermal conductivities K1 and K2 respectively are connected in series. The effective thermal conductivity of the combination is: (1) 2 K1 K2 (2) K1+K2 K1+K2 2 K1 K2 (3) K1+K2 (4) K1 K2 K1 K2 K1+K2

Q7. A uniform heavy rod of weight 10 kg m s−2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 × 1011 N m−2. Neglecting the lateral contraction, JEE Main 2021 (31 Aug Shift 1) JEE Main Previous Year Paper find the elongation of rod due to its own weight: (1) 5 × 10−10 m (2) 4 × 10−8 m (3) 5 × 10−8 m (4) 2 × 10−9 m

Q7. The R.M.S. speeds of the molecules of Hydrogen, Oxygen, and Carbon dioxide at the same temperature are vH, vO and vC respectively, then: (1) vC > vO > vH (2) vH = vO > vC (3) vH > vO > vC (4) vH = vO = vC

Q7. Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 × 103 kg . The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, JEE Main 2021 (31 Aug Shift 2) JEE Main Previous Year Paper calculate the compression strain of each column. [use 𝑌= 2 . 0 × 1011 Pa, 𝑔= 9 . 8 m s-2] (1) 1 . 87 × 10-3 (2) 2 . 60 × 10-7 (3) 3 . 60 × 10-8 (4) 7 . 07 × 10-4

Q7. The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is L. The magnitude of the areal velocity of the planet is : JEE Main 2021 (18 Mar Shift 2) JEE Main Previous Year Paper (1) 4L (2) L M M (3) 2L (4) L M 2M

Q7. An ideal gas is expanding such that PT 3 = constant. The coefficient of volume expansion of the gas is: (1) T2 (2) T3 (3) T1 (4) T4

Q7. The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9. 0 × 103 km. Find the mass of Mars. { Given 4π2G = 6 × 1011 N−1 m−2 kg2} (1) 5. 96 × 1019 kg (2) 3. 25 × 1021 kg (3) 7. 02 × 1025 kg (4) 6. 00 × 1023 kg

Q7. Two discs have moments of intertia I1 and I2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, ω1 and ω2 respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by: (1) I1I2 (ω1 −ω2)2 (2) (ω1−ω2)2 (I1+I2) 2(I1+I2) (3) I1I2 (ω1 −ω2)2 (4) (I1−I2)2ω1ω2 2(I1+I2) 2(I1+I2)

Q7. A body takes 4 min to cool from 61°C to 59°C. If the temperature of the surroundings is 30°C, the time taken by the body to cool from 51°C to 49°C is: (1) 4 min. (2) 3 min. (3) 8 min. (4) 6 min.

Q7. If 𝑌, 𝐾 and 𝜂 are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters. 9 𝐾𝜂 3𝑌𝐾 (1) 𝑌= m-2 (2) 𝜂= m-2 3 𝐾- 𝜂N 9𝐾+ 𝑌N (3) 𝐾= 𝑌𝜂 N m-2 (4) 𝑌= 9 𝐾𝜂 N m-2 9𝜂- 3𝑌 2𝜂+ 3 𝐾

Q7. A cord is wound round the circumference of wheel of radius r, The axis of the wheel is horizontal and the moment of inertia about it is I . A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance h, the square of angular velocity of wheel will be (1) 2mgh (2) 2mgh I+mr2 I+2mr2 (3) 2gh (4) I+mr22gh

Q8. Each side of a box made of metal sheet in cubic shape is 𝑎 at room temperature 𝑇, the coefficient of linear expansion of the metal sheet is 𝛼. The metal sheet is heated uniformly, by a small temperature 𝛥𝑇, so that its new temperature is 𝑇+ 𝛥𝑇. Calculate the increase in the volume of the metal box. (1) 4𝑎3𝛼𝛥𝑇 (2) 3𝑎3𝛼𝛥𝑇 (3) 4𝜋𝑎3𝛼𝛥𝑇 (4) 43𝜋𝑎3𝛼𝛥𝑇

Q8. Consider a binary star system of star A and star B with masses mA and mB revolving in a circular orbit of radii rA and rB, respectively. If TA and TB are the time period of star A and star B, respectively, then: (1) TA rA 23 (2) TA = TB = TB ( rB ) (3) TA > TB (if mA > mB ) (4) TA > TB (if rA > rB )

Q8. A mass of 50 kg is placed at the center of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the center is V kg m−1 . The value of V is: (1) +2G (2) −20G (3) −4G (4) −60G

Q8. If one mole of the polyatomic gas is having two vibrational modes and β is the ratio of molar specific heats for polyatomic gas (β = CPCv ) then the value of β is : (1) 1. 02 (2) 1. 2 (3) 1. 25 (4) 1. 35

Q8. T0 is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to 161 times of its initial value, the modified time period is (1) T0 (2) 8πT0 (3) 4T0 (4) 14 T0

Q8. A heat engine has an efficiency of 1 . When the temperature of sink is reduced by 62°C, its efficiency get 6 doubled. The temperature of the source is : (1) 124°C (2) 37°C (3) 62°C (4) 99°C JEE Main 2021 (25 Jul Shift 2) JEE Main Previous Year Paper

Q8. The normal density of a material is ρ and its bulk modulus of elasticity is K . The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be : (1) PKρ (2) ρPK (3) ρKP (4) ρPK

Q8. A glass tumbler having inner depth of 17 . 5 cm is kept on a table. A student starts pouring water 𝜇= 4 into it 3 while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled ? (1) 10 cm (2) 11 . 7 cm (3) 7 . 5 cm (4) 8 . 75 cm JEE Main 2021 (01 Sep Shift 2) JEE Main Previous Year Paper

Q8. A reversible engine has an efficiency of 1 . If the temperature of the sink is reduced by 58°C, its efficiency 4 becomes double. Calculate the temperature of the sink: (1) 180. 4°C (2) 382°C (3) 174 K (4) 280°C

Q8. Two thin metallic spherical shells of radii 𝑟1 and 𝑟2𝑟1 < 𝑟2 are placed with their centres coinciding. A material of thermal conductivity 𝐾 is filled in the space between the shells. The inner shell is maintained at temperature 𝜃1 and the outer shell at temperature 𝜃2𝜃1 < 𝜃2 . The rate at which heat flows radially through the material is : (1) 𝐾𝜃2 - 𝜃1 (2) 𝐾𝜃2 - 𝜃1𝑟2 - 𝑟1 𝑟2 - 𝑟1 4𝜋𝑟1𝑟2 (3) 𝜋𝐾𝑟1𝑟2𝜃2 - 𝜃1 (4) 4𝜋𝐾𝑟1𝑟2𝜃2 - 𝜃1 𝑟2 - 𝑟1 𝑟2 - 𝑟1

Q8. In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A →B and C →D are T1 and T2( T 1 > T2) respectively. JEE Main 2021 (27 Jul Shift 1) JEE Main Previous Year Paper Choose the correct option out of the following for work done if processes BC and DA are adiabatic. (1) WAB = WDC (2) WAD = WBC (3) WBC + WDA > 0 (4) WAB < WCD

Q8. The temperature of equal masses of three different liquids x, y and z are 10°C, 20°C and 30°C respectively. The temperature of mixture when x is mixed with y is 16°C and that when y is mixed with z is 26°C. The temperature of mixture when x and z are mixed will be : (1) 25. 62°C (2) 20. 28°C (3) 28. 32°C (4) 23. 84°C