Practice Questions

Q7. A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is: (1) F (2) 3F 3 mR 2 m R (3) 2F (4) F 3 m R 2 m R

Q7. The ratio of the weights of a body on Earth’s surface to that on the surface of a planet is 9 : 4 The mass of the planet is 1 th of that of the Earth. If R is the radius of the Earth, what is the radius of the planet? (Take the 9 planets to have the same mass density) (1) R (2) R 4 2 (3) R (4) R 3 9

Q7. An 𝐿 -shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If 𝐴𝐵= 𝐵𝐶, and the angle made by 𝐴𝐵 with downward vertical is 𝜃, then: 2 1 (1) tan⁡𝜃= (2) tan⁡𝜃= √3 3 (3) tan⁡𝜃= 1 (4) tan⁡𝜃= 1 2 2√3

Q7. Moment of inertia of a body about a given axis is 1.5 kg m2. Initially the body is at rest. In order to produce a rotational kinetic energy of 1200 J, the angular acceleration of 20 rad/s2 must be applied about the axis for a duration of: (1) 3 s (2) 2 s (3) 2.5 s (4) 5 s

Q7. A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis. When released from the initial horizontal position, its instantaneous angular acceleration will be (1) g (2) 7g 2l 3l (3) 3lg (4) 13lg

Q7. The energy required to take a satellite to a height h above the Earth surface (radius of Earth = 6.4 × 103 km ) is E1 , and the kinetic energy required for the satellite to be in a circular orbit at this height is E2. The value of h for which E1 and E2 are equal, is (1) 1.28 × 104km (2) 6.4 × 103km (3) 3.2 × 103km (4) 1.6 × 103km

Q7. The ratio of surface tensions of mercury and water is given to be 7.5 , while the ratio of their densities is 13.6 . Their contact angles, with glass, are close to 135° and 0° , respectively. If it is observed that mercury gets depressed by an amount h in a capillary tube of radius r1 , while water rises by the same amount h in a capillary tube of radius r2 , then the ratio r1 is close to r2 (1) 3 (2) 2 5 3 (3) 4 (4) 2 5 5

Q7. A circular disc of radius 𝑏 has a hole of radius a at its centre(see figure). If the mass per unit area of the disc 𝜎0 varies as then, the radius of gyration of the disc about its axis passing through the center is 𝑟 (1) 𝑎+ 𝑏 (2) + 𝑏2 + 𝑎𝑏 3 √𝑎2 3 + 𝑏2 + 𝑎𝑏 (3) 𝑎+ 𝑏 (4) √𝑎2 2 2

Q7. The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane: (i) a ring of radius R, (ii) a solid cylinder of radius R2 and (iii) a solid sphere of radius R4 . If, in each case, the speed of the center of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is: JEE Main 2019 (09 Apr Shift 1) JEE Main Previous Year Paper (1) 2 : 3 : 4 (2) 20 : 15 : 14 (3) 4 : 3 : 2 (4) 14 : 15 : 20

Q8. A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K1 and that of the outer cylinder is K2 . Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is: (1) 2K1+3K2 (2) K1+K2 5 2 (3) K1 + K2 (4) K1+3K24

Q8. A liquid of density ρ is coming out of a hose pipe of radius a with horizontal speed v and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be: (1) 1 ρv2 (2) 3 ρv2 4 4 (3) 1 ρv2 (4) ρv2 2

Q8. A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet? [Given: Mass of planet = 8 × 1022 kg , Radius of planet = 2 × 106 m, Gravitational constant G = 6.67 × 10-11 Nm2 / kg2 ] (1) 17 (2) 9 (3) 13 (4) 11

Q8. Two stars of masses 3 × 1031 kg each, and at distance 2 × 1011 m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the stars,s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is ( Take Gravitational constant G = 6.67 × 10−11 N m2 kg−2 ) (1) 2.4 × 104 m s−1 (2) 3.8 × 104 m s−1 (3) 2.8 × 105 m s−1 (4) 1.4 × 105 m s−1

Q8. A solid sphere of mass M and radius a is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance 3a from the centre will be: (1) GM (2) GM 9a2 3a2 (3) 2GM (4) 2GM 3a2 9a2

Q8. A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is: (1) 23 m v2 (2) m v2 (3) 12 m v2 (4) 2 m v2

Q8. Two rods A and B of identical dimensions are at temperature 30∘C. If A is heated upto 180∘C and B upto T∘C, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is (1) 230∘C (2) 270∘C (3) 200∘C (4) 250∘C

Q8. A test particle is moving in a circular orbit in the gravitational field produced by a mass density ρ(r) = K . r2 Identify the current relation between the radius R of the particle’s orbit and its period T : JEE Main 2019 (09 Apr Shift 2) JEE Main Previous Year Paper (1) TR is a constant (2) T 2/R3 is a constant (3) T/R is a constant (4) T/R2 is a constant

Q8. A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights ℎ𝑠𝑝ℎ and ℎ𝑐𝑦𝑙 on the inline. The ratio JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper ℎ𝑠𝑝ℎ is given by: ℎ𝑐𝑦𝑙 2 4 (1) (2) √5 5 (3) 14 (4) 1 15

Q8. A solid sphere, of radius R acquires a terminal velocity v1 when falling (due to gravity) through a viscous fluid having a coefficient of viscosity η. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v2, when falling through the same fluid, the ratio ( v1v2 ) equals: (1) 1 (2) 27 9 (3) 1 (4) 9 27

Q8. If the angular momentum of a planet of mass 𝑚, moving around the Sun in a circular orbit is 𝐿, about the center of the Sun, its areal velocity is: (1) 𝐿 (2) 4𝐿 𝑚 𝑚 𝐿 2𝐿 (3) (4) 2𝑚 𝑚

Q8. The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m3 water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to: (1) 2.9 m (2) 4.8 m (3) 6.0 m (4) 9.6 m

Q8. n moles of an ideal gas with constant volume heat capacity Cv undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is: (1) 4nR (2) 4nR Cv+nR Cv−nR (3) nR (4) nR Cv+nR Cv−nR

Q9. Ice at −20∘C is added to 50 g of water at 40∘C, When the temperature of the mixture reaches 0∘C, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2 J/g/∘C Specific heat of Ice = 2.1 J/g/∘C Heat of fusion of water at 0∘C = 334 J/g) (1) 50 g (2) 100 g (3) 60 g (4) 40 g

Q9. A steel wire having a radius of 2.0 mm , carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1π m s-2, what will be the tensile stress that would be developed in the wire? (1) 5.2 × 106 N m-2 (2) 6.2 × 106 N m-2 (3) 4 . 8 × 106 N m-2 (4) 3.1 × 106 N m-2

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