Practice Questions

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. A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass 'm' at x = 0, if the mass per unit length of the rod is A + Bx2, is given by: JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper (1) Gm[A( a+L1 −1a ) + BL] (2) Gm[A( a+L1 −1a ) −BL] (3) Gm[A( a1 − a+L1 ) −BL] (4) Gm[A( a1 − a+L1 ) + BL]

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. A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the center and the sides, in cm, will be: (1) 0.4 (2) 2.0 (3) 1.2 (4) 0.1

Q7. The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be: (1) √3 2 s (2) √32 s (3) 3 s (4) 2√3 s 2

Q7. A satellite is revolving in a circular orbit at a height h from the carth surface, such that h << R where R is the radius of the earth. Assuming that the effect of earth"s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is (1) √2gR (2) √gR (3) √gR2 (4) √gR(√2 −1)

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

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. 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 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. 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. 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

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. A boy’s catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms-1 . Neglect the change in the area of cross-section of the cord while stretched. The Young’s modulus of rubber is closest to: (1) 106N m-2 (2) 104N m-2 (3) 108N m-2 (4) 103N m-2

Q8. The moment of inertial of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is ′I(x)′. Which one of the graphs represents the variation of I(x) with x correctly? (1) (2) (3) (4)

Q8. At 40°C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40°C to 20°C it regains its original length of 0.2 m . The value of M is close to: (Coefficient of linear expansion and Young’s modulus of brass are 10-5 /° C and 1011 N / m2, respectively; g = 10 m s-2 ) (1) 0.9 kg (2) 0.5 kg (3) 1.5 kg (4) 9 kg

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. 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 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 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. 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. 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. 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

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. 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