Practice Questions

Q4. A thin disc of mass M and radius R has mass per unit area σ(r) = kr2 where r is the distance from its centre. Its moment inertia about an axis going through its centre of mass and perpendicular to its plane is: (1) MR2 (2) MR2 3 2 (3) MR2 (4) 2MR2 6 3

Q4. A body of mass 1 kg falls freely from a height of 100 m, on a platform of mass 3 kg which is mounted on a spring having spring constant k = 1.25 × 106 N/m. The bodysticks to the platform and the spring's maximum compression is found to be x. Given that g = 10 ms−2, the value of x will be close to : (1) 40 cm (2) 4 cm (3) 80 cm (4) 8 cm −−−Q5. → → → A slab is subjected to two forces F1 and F2 of same magnitude F as shown in the figure. Force F2 is in XY- plane while force F1 acts along z -axis at the point (2→i + 3→j). The moment of these forces about point O will be: (1) (3^i −2^j + 3^k) F (2) (3^i −2^j −3^k)F (3) (3^i + 2^j −3^k)F (4) (3^i + 2^j + 3^k)F

Q4. The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force acting on it is 1 N, and the distance of the particle from the origin is 5 m, the angle between the force and the position vector is (in radians): (1) π (2) π 6 3 (3) π (4) π 8 4

Q4. A block of mass 𝑚, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant 𝑘. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force 𝐹, the maximum speed of the block is: 𝐹 2𝐹 (1) (2) √𝑚𝑘 √𝑚𝑘 (3) 𝜋𝐹 (4) 𝐹 √𝑚𝑘 𝜋√𝑚𝑘

Q4. If 1022 gas molecules each of mass 10-26 kg collides with a surface (perpendicular to it) elastically per second over an area 1 m2 with a speed 104m / s, the pressure exerted by the gas molecules will be of the order of: (1) 2 Pa (2) 4 Pa (3) 6 Pa (4) 8 Pa

Q4. The position vector of the center of mass→rcm of an asymmetric uniform bar of negligible area of cross-section as shown in figure is: 13 (1)→rcm = 8 L^x + 85 Lˆy (2)→rcm = 8 5 L^x + 138 Lˆy 11 (3) →rcm = 8 3 L^x + 118 Lˆy (4)→rcm = 8 L^x + 83 Lˆy

Q4. A block of mass m is kept on a platform which starts from rest with a constant acceleration g/2 upwards, as shown in the figure. Work done by normal reaction on block in time t is (1) −mg2t28 (2) m g2t28 (3) 0 (4) 3 m g2t2 8

Q4. Two blocks A and B of masses mA = 1 kg and mB = 3 kg are kept on the table as shown in figure. The coefficients of friction between A and B is 0.2 and between B and the surface of the table is also 0.2 . The maximum force F that can be applied on B horizontally, so that the block A does not slide over the block B is : [Take g = 10 m / s2 ] (1) 16 N (2) 12 N (3) 40 N (4) 8 N 7M

Q4. A spring whose unstrentches length is l has a force constant k. The spring is cut into two pieces of unstretches lengths l1 and l2 where, l1 = nl2 and n is an integer. The ratio k1/k2 of the corresponding force constants, k1 and k2 will be: (1) 1 (2) n2 n2 (3) n (4) n1

Q4. A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above piston is l1, and that below the piston is l2, such that l1 > l2. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass m will be given by: ( R is universal gas constant and g is the acceleration due to gravity) (1) RT l1−3l2 (2) nRT l1−l2 ng [ l1l2 ] g [ l1l2 ] (3) RT 2l1+l2 (4) RT 2l1+l2 g [ l1l2 ] gl [ l1l2 ]

Q4. A man (mass = 50 kg ) and his son (mass = 20 kg ) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 m s-1 with respect to the man. The speed of the man with respect to the surface is: (1) 0.20 m s-1 (2) 0.14 m s-1 (3) 0.47 m s-1 (4) 0.28 m s-1

Q4. A uniform cable of mass M and length L is placed on a horizontal surface such that its ( n1 ) th below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be: (1) MgL (2) MgL 2n2 n2 (3) nMgL (4) 2MgL n2

Q4. A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by: (1) v2 (2) v2 g 2g (3) 2v2 (4) 2v2 5g 7g

Q4. A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45° at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g = 10 m s−2) (1) 100 N (2) 200 N (3) 140 N (4) 70 N

Q5. A particle which is experiencing a force, given by F = 3ˆi −12ˆj, undergoes a displacement of d = 4ˆi. If the particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy at the end of the displacement? (1) 9 J. (2) 15 J. (3) 12 J. (4) 10 J.

Q5. A uniform rectangular thin sheet 𝐴𝐵𝐶𝐷 of mass 𝑀 has length 𝑎 and breadth 𝑏, as shown in the figure. If the shaded portion 𝐻𝐵𝐺𝑂 is cut-off, the coordinates of the centre of mass of the remaining portion will be: (1) 5a 5b (2) 5a , 5b 12, 12 3 3 (3) 2a , 2b (4) 3a , 3b 3 3 4 4

Q5. A person of mass 𝑀 is sitting on a swing of length 𝐿 and swinging with and an angular amplitude θ0 . If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance 𝑙 𝑙< < 𝐿, is close to: (1) 𝑀𝑔𝑙 (1 - θ02 ) (2) θ02 𝑀𝑔𝑙(1 + ) 2 (3) 𝑀𝑔𝑙 (4) 𝑀𝑔𝑙(1 + θ02 )

Q5. A particle of mass m is moving with speed 2v and collides with a mass 2m moving with speed v in the same direction. After the collision, the first mass is stopped completely while the second one splits into two particles each of mass m, which move at an angle 45o with respect to the original direction. The speed of each of the moving particle will be (1) √2v (2) v √2 (3) 2√2v (4) v (2√2)

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. 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. Two coaxial discs, having moments of inertia I1 and I12 , are rotating with respective angular velocities ω1 and ω1 , about their common axis. They are brought in contact with each other and thereafter they rotate with a 2 common angular velocity. If Ef and Ei are the final and initial total energies, then (Ef −Ei) is: (1) I1ω2 1 (2) 3 8 I1ω21 6 1 (3) − I1ω212 1 (4) − I1ω224 JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper

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

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. 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 string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string) (1) 20rad/s2 (2) 16rad/s2 (3) 12rad/s2 (4) 10rad/s2