Centre of Mass & Momentum PYQs Set 3 (PDF)

Set 3 of 4 · Questions 61-90 of 103

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Mere Teacher · Previous Year Questions JEE Main Physics · Centre of Mass & Momentum · Set 3 (Q61-90)
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61. $A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle of inclination 30º. The centre of mass of the cylinder has speed of 4 m/s. The distance travelled by the cylinder on the inclined surface will be, [take g = 10 m/ s^{2}]$ (1) $2.2 m$ (2) $1.6 m$ (3) $1.2 m$ (4) $2.4 m$ 62. $Three identical spheres each of mass 1 kg are placed touching one another with their centres in a straight line. Their centres are marked as A, B, C respectively. The distance of centre of mass of the system from A is$ (1) $\frac{AB + AC}{2}$ (2) $\frac{AB + BC}{2}$ (3) $\frac{AC - AB}{3}$ (4) $\frac{AB + AC}{3}$ 63. $A small disc of mass 500 g and radius 5 cm rolls down an inclined plane without slipping. Speed of its centre of mass when it reaches the bottom of the inclined plane depends on$ (1) $mass and radius$ (2) $mass and height of the incline$ (3) $height of the incline$ (4) $height of the incline and acceleration due to gravity$ 64. $In figure E and V_{cm} represent the total energy and speed of centre of mass of an object of mass 1 kg in pure rolling. The object is$ (1) $sphere$ (2) $ring$ (3) $disc$ (4) $hollow cylinder.$ 65. $Two particles of masses 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass. The center of mass of the system from the 5 kg particle is nearly at a distance of [NEET 2020]$ (1) $50 cm$ (2) $67 cm$ (3) $80 cm$ (4) $33 cm$ 66. $A huge circular arc of length 4.4ly subtends an angle '4s' at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second ?$ (1) $4.1 \times 1 0^{8} s$ (2) $4.5 \times 1 0^{10} s$ (3) $3.5 \times 1 0^{6} s$ (4) $7.2 \times 1 0^{8} s$ 67. $Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The center of mass of the system is at a point :$ (1) $0.6 cm right and 2.0 cm above 1kg mass$ (2) $2.0 cm right and 0.9 cm above 1 kg mass$ (3) $0.9 cm right and 2.0 cm above 1kg mass$ (4) $1.5 cm right and 1.2 cm above 1kg mass$ 68. $56. A rod of length is 3m and its mass acting per unit length is directly proportional to distance x from one of its end then its centre of gravity from that end will be at$ (1) $1.5 m$ (2) $2 m$ (3) $2.5 m$ (4) $3.0 m .$ 69. $A particle of mass 10 g is moving towards east with a velocity of 10 ms^{- 1} and another particle of mass 15 g is moving towards north with a velocity of 5 ms^{- 1} . The magnitude of the velocity of the centre of mass of the system of the two particles is$ (1) $5 ms^{- 1}$ (2) $10 ms^{- 1}$ (3) $15 ms^{- 1}$ (4) $7.5 ms^{- 1}$ 70. $A metre stick is balanced on a knife edge at its centre. When four coins, each of mass 2 g are put one on top of the other at 10.0 cm mark, the stick it found to be balanced at 46.0 cm mark. The mass of the metre stick is$ (1) $66 g$ (2) $60 g$ (3) $72 g$ (4) $18 g$ 71. $Four masses are arranged along a circle of radius 1 m as shown in the figure. The centre of mass of this system of masses is at$ (1) $- \frac{1}{5} i - \frac{1}{5} \cdot j$ (2) $\frac{1}{5} i + j$ (3) $i - \frac{1}{5} j$ (4) $\frac{1}{5} i + \frac{1}{5} j$ 72. $A stone is tied to a string of length l and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed u . The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is$ (1) $2 (u^{2} - gl)$ (2) $u^{2} - gl$ (3) $u - u^{2} - 2 gl$ (4) $2 gl$ 73. $A particle of mass 5 m at rest suddenly breaks on its own into three fragments. Two fragments of mass m, each move along mutually perpendicular direction with each speed v . The energy released during the process is [NEET 2019]$ (1) $\frac{3}{5} m v^{2}$ (2) $\frac{5}{3} m v^{2}$ (3) $\frac{3}{2} m v^{2}$ (4) $\frac{4}{3} m v^{2}$ 74. $Three identical spheres, each of mass M, are placed at the corners of a right-angle triangle with the mutually perpendicular sides equal to 2 m (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of center of mass. [NEET 2020]$ (1) $2 (i + j)$ (2) $(i + j)$ (3) $23 (i + j)$ (4) $43 (i + j)$ 75. $Three identical metal balls, each of the radius r^{:} are placed touching each other on a horizontal surface such that an equilateral triangle is formed when centres of three balls are joined. The centre of the mass of the system is located at$ (1) $line joining centres of any two balls$ (2) $centre of one of the balls$ (3) $horizontal surface$ (4) $point of intersection of the medians.$ 76. $A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time a bullet of mass 0.02 kg is fired vertically upwards, with a velocity 100 m s^{-1} from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is : (g = 10 m/ s^{-2})$ (1) $10 m$ (2) $20 m$ (3) $30 m$ (4) $40 m$ 77. $Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m which C has mass M. Block A is given an initial speed v towards B due to which it collides with B perfectly inelastically. The combined mass collides with C, also perfectly inelastically \frac{5}{6} t h of the initial kinetic energy is lost in whole process. What is value of M/m ?$ (1) $2$ (2) $4$ (3) $5$ (4) $3$ 78. $The sum of moments of all the particles in a system about its centre of mass is always$ (1) $minimum$ (2) $zero$ (3) $maximum$ (4) $infinite$ 79. $A mass attached to one end of a string crosses top. most point on a vertical circle with critical speed. Its centripetal acceleration, when string becomes horizontal will be (g = gravitational acceleration)$ (1) $g$ (2) $3 g$ (3) $4 g$ (4) $6 g$ 80. $Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is:$ (1) $3:4$ (2) $9 : 16$ (3) $16 : 9$ (4) $4 : 3$ 81. $Body A of mass 4 m moving with speed u collides with another body B of mass 2 m at rest the collision is head on and elastic in nature. After the collision the fraction of energy lost by colliding body A is :$ (1) $\frac{5}{9}$ (2) $\frac{1}{9}$ (3) $\frac{8}{9}$ (4) $\frac{4}{9}$ 82. $A rod of length 5 L is bent right angle keeping one side length as 2 L. The position of the center of mass of the system: (Consider L = 10 cm)$ (1) $4 i + 9 j$ (2) $2 i + 3 j$ (3) $5 i + 8 j$ (4) $3 i + 7 j$ 83. $The ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. I_{AB}, I_{BC} and I_{CA} are the moments of inertia of the plate about AB, BC and CA respectively. Which one of the following relations is correct?$ (1) $I_{AB} + I_{BC} = I_{CA}$ (2) $I_{CA} is maximum$ (3) $I_{AB} > I_{BC}$ (4) $I_{BC} > I_{AB} .$ 84. $Consider a uniform rod of mass M = 4m and length λ pivoted about its centre. A mass m moving with velocity v making angle θ = \frac{π}{4} to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is:$ (1) $\frac{4}{7} \frac{v}{ℓ}$ (2) $\frac{3 2}{7} \frac{v}{ℓ}$ (3) $\frac{3}{7} \frac{v}{ℓ}$ (4) $\frac{3}{7 2} \frac{v}{ℓ}$ 85. $A simple pendulum, made of a string of length λ and a bob of mass m, is released from a small angle θ_{0} . It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ_{1} . Then M is given by :$ (1) $m (\frac{θ _{0} + θ _{1}}{θ _{0} - θ _{1}})$ (2) $\frac{m}{2} (\frac{θ _{0} - θ _{1}}{θ _{0} + θ _{1}})$ (3) $\frac{m}{2} (\frac{θ _{0} + θ _{1}}{θ _{0} - θ _{1}})$ (4) $m (\frac{θ _{0} - θ _{1}}{θ _{0} + θ _{1}})$ 86. $Which of the points is likely position of the centre of mass of the system shown in the figure?$ (1) $A$ (2) $D$ (3) $B$ (4) $C$ 87. $A uniform rod of length l is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T (x) at a distance x from the axis, then which of the following graphs depicts it most closely?$ (1) (2) (3) (4) 88. $Two particles of masses 1 g and 2 g move towards each other with velocities 10 m s^{- 1} and 20 m s^{- 1} respectively. The velocity of the centre of mass of the system of the two particles is$ (1) $5 ms^{- 1}$ (2) $10 ms^{- 1}$ (3) $15 ms^{- 1}$ (4) $20 ms^{- 1}$ 89. $A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment ofinertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is____\times 10^{- 1} kg m^{2}$ 90. $In a system two particles of masses m_{1} = 3 kg and m_{2} = 2 kg are placed at certain distance from each other. The particle of mass m_{1} is moved towards the center of mass of the system through a distance 2 cm . In order to keep the center of mass of the system at the original position, the particle of mass m_{2} should move towards the center of mass by the distance______cm .$