Practice Questions

Q5. A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body? (1) 1.8 kg (2) 1.2 kg (3) 1.0 kg (4) 1.5 kg

Q5. Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The (x, y) coordinates of the centre of mass will be: √3 √3 m, m, (1) ( 127 4 m) (2) ( 127 8 m) (3) ( √34 m, 125 m) (4) ( √38 m, 127 m)

Q5. A force acts on a 2 kg object so that its position is given as a function of time as x = 3t2 + 5. What is the work done by this force in first 5 seconds? (1) 875 J (2) 850 J (3) 950 J (4) 900 J

Q5. A particle of mass 20 g is released with an initial velocity 5 m s−1 along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper the particle reaches point B, its angular momentum about O will be: (Take g = 10 m s−2 ) (1) 3 kg m2 s−1 (2) 2 kg m2 s−1 (3) 6 kg m2 s−1 (4) 8 kg m2 s−1

Q5. Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm ), about its axis be I . The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is: (1) 16 cm (2) 14 cm (3) 12 cm (4) 18 cm

Q6. An equilateral triangle ABC is cut from a thin solid sheet of wood. (See figure) D, E and F are the mid-points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I0 . If the smaller triangle DEF is removed JEE Main 2019 (11 Jan Shift 1) JEE Main Previous Year Paper from ABC, the moment of inertia of the remaining figure about the same axis is I . Then (1) I = 1516 I0 (2) I = 43 I0 (3) I = 169 I0 (4) I = I04

Q6. Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is JEE Main 2019 (10 Jan Shift 2) JEE Main Previous Year Paper (1) 209 MR2 . (2) 152 MR2 . 15 15 (3) 137 MR2 . (4) 17 MR2 . 15 5

Q6. A smooth wire of length 2πr is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed ω about the vertical diameter AB, as shown in figure, the JEE Main 2019 (12 Apr Shift 2) JEE Main Previous Year Paper bead is at rest with respect to the circular ring at position P as shown. Then the value of ω2 is equal to: (1) 2g/r (2) √3g 2r (3) 2g/(r√3) (4) (g√3)/r

Q6. An alpha- particle of mass m suffers 1- dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing 64% of its initial kinetic energy. The mass of the nucleus is (1) 1.5m (2) 4m (3) 3.5m (4) 5m

Q6. A body of mass 𝑚1 moving with an unknown velocity of 𝑣1 ^i, undergoes a collinear collision with a body of mass 𝑚2 moving with a velocity 𝑣2 ^i . After the collision, 𝑚1 and 𝑚2 move with velocities of 𝑣3 ^i and 𝑣4 ^i, respectively. If 𝑚2 = 0.5 𝑚1 and 𝑣3 = 0.5 𝑣1, then 𝑣1 is: 𝑣2 𝑣2 (1) 𝑣4 - 4 (2) 𝑣4 - 2 (3) 𝑣4 + 𝑣2 (4) 𝑣4 - 𝑣2

Q6. A uniform rod of length 𝑙 is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T ( 𝑥) at a distance 𝑥 from the axis, then which of the following graphs depicts it most closely? (1) (2) (3) (4) JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper

Q6. A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about AB at 25 rotations per second in 5 s , is close to: (1) 1.6 × 10-5 N m (2) 2.0 × 10-5 N m (3) 7.9 × 10-6 N m (4) 4.0 × 10-6 N m

Q6. A circular disc D1 of mass M and radius R has two identical discs D2 and D3 of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO', passing through the centre of D1 , as shown in the figure, will be JEE Main 2019 (11 Jan Shift 2) JEE Main Previous Year Paper (1) MR2 (2) 3MR2 (3) 5 4 MR2 (4) 32 MR2

Q6. A thin smooth rod of length L and mass M is rotating freely with angular speed ω0 about an axis perpendicular to the rod and passing through center. Two beads of mass m and negligible size are at the center of the rod initially. The beads of mass m and negligible size are at the center of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod, will be: (1) M ω0 (2) M ω0 M+3m M+2m (3) M ω0 (4) M ω0 M+6m M+m

Q6. A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle of 30o from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s−1 ) will be (g = 10 ms−2) JEE Main 2019 (09 Jan Shift 2) JEE Main Previous Year Paper (1) √20 (2) √30 3 2 (3) √302 (4) √30

Q6. To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is μ, the torque, applied by the machine on the mop is: (1) 2 μFR/3 (2) μFR/3 (3) μFR/6 (4) μFR/2

Q6. A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of θ, where θ is the angle by which it has rotated, is given as kθ2 . If its moment of inertia is I then the angular acceleration of the disc is: (1) 2k θ (2) k θ I 2I (3) k θ (4) k θ 4I I

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 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 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 time dependence of the position of a particle of mass m = 2 is given by →rt = 2t ^i - 3t2^j . Its angular momentum, with respect to the origin, at time t = 2 is: (1) 36 ^k (2) 48 ^i + ^j (3) -48 ^k (4) -34 ^k - ^i

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. 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. 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. 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