Practice Questions

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. A satellite of mass M is in a circular orbit of radius R about the center of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastic. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be: (1) In an elliptical orbit (2) Such that it escapes to infinity (3) In a circular orbit of a different radius (4) In the same circular orbit of radius R

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 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. 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 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. 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. 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 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

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 thin circular plate of mass 𝑀 and radius 𝑅 has its density varying as ρ ( 𝑟) =ρ0r with 𝜌0 as constant and 𝑟 is the distance from its centre. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is 𝐼= 𝑎𝑀𝑅2. The value of the coefficient 𝑎 is: (1) 3 (2) 1 (3) 8 (4) 3 5 2 5 2

Q6. Two masses 𝑚 and are connected at the two ends of a massless rigid rod of length 𝑙. The rod is suspended by 2 a thin wire of torsional constant 𝑘 at the centre of mass of the rod-mass system (see figure). Because of torsional constant 𝑘, the restoring torque is 𝜏= 𝑘𝜃 for angular displacement 𝜃. If the rod is rotated by 𝜃0 and released, JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper the tension in it when it passes through its mean position will be: (1) 𝑘𝜃02 (2) 3𝑘𝜃02 𝑙 (3) 2𝑘𝜃02 (4) 𝑘𝜃02 𝑙 𝑙

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. 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. The value of acceleration due to gravity at Earth's surface is 9.8 m s−2 . The altitude above its surface at which the acceleration due to gravity decreases to 4.9 m s−2 , is close to: (Radius of earth = 6.4 × 106 m ) (1) 1.6 × 106 m (2) 2.6 × 106 m (3) 6.4 × 106 m (4) 9.0 × 106 m

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

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. 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 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 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. 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. 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. 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. Four identical particles of mass M are located at the corners of a square of side ‘𝑎’ . What should be their speed if each of them revolves under the influence of other’s gravitational field in a circular orbit circumscribing the JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper square? (1) GM (2) GM (3) GM (4) GM 1.35√ a 1.21√ a 1.41√ a 1.16√ a