System Of Particles And Rotational Motion MCQs and Answers will be useful for various entrance exam like NEET, AIIMS, JEE. It includes an extensive section of physics and chemistry. These chapter covers each and every topic of System of Particles and Rotational Motion and more. It also contains chapter-wise MCQs with hints and options to make your preparation easy.
System Of Particles And Rotational Motion MCQs and Answers
These System Of Particles And Rotational Motion MCQs and Answers are based on the following topics:
System Of Particles And Rotational Motion MCQs
1. A body is under an angular deceleration of 5rad/s2. Its initial speed is 3rad/s. How much angular distance ‘θ’ will it cover before coming to rest?
a) 0.8 rad
b) 0.9 rad
c) 9 rad
d) 2 rad
2. A ring of diameter 1m is rotating about a central axis perpendicular to its diameter. It is rotating with a speed of 10rad/s. What force should be applied on it tangentially to stop it in exactly 3 rotations? Let the mass of the ring be 2kg.
a) 10 N
b) 25/3π N
c) 50/3π N
d) 12.5/3 N
3. The angular acceleration of a body = 3t2. What will be its speed at t=10s, if initial speed = 10rad/s?
a) 1010 rad/s
b) 300 rad/s
c) 1310 rad/s
4. The rate of change of angular speed is constant. What will be the expression for change in angular speed after time dt, if angular acceleration is ‘a’? The initial angular speed is ‘w’.
b) w – a*dt
c) w + a*dt
d) There is no change
5. The angular speed of a body is 2rpm. What should be the angular acceleration for the angular speed to double up in 5s?
a) -2π/75 rad/s2
b) -π/75 rad/s2
c) π/75 rad/s2
d) 2π/75 rad/s2
6. A body has a moment of inertia = 5kgm2 about an axis. What should be the torque for increasing its angular speed from 0 to 10rad/s in 4s? Assume that the body rotates purely about that axis.
7. Masses 1 kg, 1.5 kg, 2 kg, and “M” kg are situated at (2,1,1), (1,2,1), (2,-2,1) and (-1,4,3). What is the value of “M” if their centre of mass is at (1,1,3/2)?
a) 1 kg
b) 1.5 kg
c) 2 kg
d) 2.5 kg
8. Particles of masses 1 kg and 3 kg are at (2i+5j+13k) m and (-6i+4j-2k) m. What is the position of their centre of mass?
a) 1/4 (-16i + 17j + 7k) m
b) 1/4 (-8i + 17j + 7k) m
c) 1/4 (-6i + 17j + 7k) m
d) 1/4 (-6i + 17j + 5k) m
9. The distance between the centres of carbon and oxygen in the carbon monoxide molecules is 1.13 x 10-10 m. The distance of the centre of mass of the molecule relative to the oxygen atom is _____
a) 0.48 x 10-10 m
b) 0.64 x 10-10 m
c) 0.56 x 10-10 m
d) 0.36 x 10-10 m
10. Two particles of masses 2 kg and 3 kg are at rest and are separated by 10 m. If they move towards each other under the mutual force of attraction, they would meet at _____
a) 6 m from 4 kg body
b) 6 m from 6 kg body
c) 4 m from 4 kg body
d) 5 m from 6 kg body
11. A ball of mass 3 kg and a ball of mass 2 kg roll towards each other on a flat surface. How far is the centre of mass from the 3 kg ball of the 2 balls are separated by 6 m?
a) 1.2 m
b) 2.4 m
c) 3.6 m
d) 4.8 m
12. A uniform disc of radius R is put over another uniform disc of radius 2R of same thickness and density. The edges of the two discs touch each other. What is the position of their centre of mass?
a) at 5R/3 from the centre of the larger disc
b) at 2R/3 from the centre of the larger disc
c) at 3R/5 from the centre of the larger disc
d) at 2R/5 from the centre of the larger disc
13. Three identical spheres each of radius R are placed such that their centres lie on a straight line. What is the location of their centre of mass from the centre of the first sphere?
14. A disc is standing on a flat rough surface. Its centre is suddenly given a velocity of 5m/s in the forward direction. In how much time will pure rolling start? Mass = 1kg, Radius = 10cm. Coefficient of friction = 0.4.
a) 0.25 s
b) 0.05 s
c) 0.5 s
d) 1 s
15. A solid sphere is given a horizontal velocity of 4m/s on a flat surface. What will be its velocity when it starts pure rolling? Mass = 2kg, Radius = 5cm. Coefficient of friction = 0.3.
a) It cannot roll purely
b) 2/3 s
16. A ring is at the top of the incline of angle and height ‘h’. If it is left from rest and goes down rolling purely, find its speed at the bottom.
a) √ (2gh) m/s
b) √ (gh/sinθ) m/s
c) √ (ghsinθ) m/s
d) √ (gh) m/s
17. A disc is purely rolling down an inclined plane of length ‘l’ & angle θ. What is the value of friction acting on it? Let the mass of the disc be M & radius be R.
18. A disc is under pure rolling motion on a horizontal surface. The speed of the topmost point at an instant is 5m/s w.r.t the centre of the disc. What is the velocity of the centremost point? The radius of the disc is 10cm.
19. A disc is undergoing pure rolling motion on a flat surface. The radius of the disc is 5cm & velocity of centre of mass is 10m/s. What is the ratio of kinetic energy as seen from the ground frame to a frame moving along the disc with a speed of 10m/s?
a) 1:1, kinetic energy is frame independant
20. What is the displacement of the centre of the wheel in one rotation? Let the radius of the wheel be R.
21. The velocities of three particles of masses 10 kg, 20 kg and 30 kg are 10i, 10j and 10k m/s, respectively. What is the velocity of their centre of mass?
a) (i + 2j + 3k) m/s
b) 10 (i + j + k) m/s
c) (10i + 20j + 30k) m/s
d) (3i + 2j + k) m/s
22. A system consists of 2 particles of the same mass. Let one particle be at rest and another particle have an acceleration of “2a”. What would be the acceleration of the centre of mass of the system?
23. Two particles A and B, initially at rest, start moving towards each other under a mutual force of attraction. When the speed of A is “10 m/s” and the speed of B is “800 m/s”, what is the speed of their centre of mass?
24. A uniform free rectangular steel plate is heated from 273 to 373 kelvin. The initial area of the plate is 15 sq. cm. What is the shift of the centre of mass?
b) 1 cm
c) 2 cm
d) 3 cm
25. A boy of mass 50kg is standing on a frictionless surface. He throws a ball of mass 2kg away from him with a speed of 10m/s. Find the final speed of the centre of mass.
26. A ball of mass 3kg is thrown at an angle of 30° with the horizontal & a speed of 10m/s. At the highest point the ball breaks into two parts, having mass ratio 2:1, due to internal forces. If the heavier part falls at a distance of 10m from the start, find the x coordinate of the second part.
27. A ball of mass 1kg is thrown vertically upwards from a building with a speed of 10m/s, and another ball of mass 3kg is dropped from the same point towards the ground with the same speed. At what time will the centre of mass have the maximum height w.r.t the ground? Assume balls are left at t=0.
28. A radioactive particle at rest, having mass 10g, breaks into 2 fragments (1&2) in the mass ratio 2:3 respectively. If the first one moves with a velocity of 10m/s what will be the speed of the second particle?
a) 4.33 m/s
b) -4.33 m/s
c) -6.67 m/s
d) 6.67 m/s
29. There are two external forces acting on a system of particles. Select the correct statement.
a) Linear momentum is necessarily not conserved
b) Linear momentum may be conserved
c) Linear momentum is zero
d) Centre of mass will move with increasing speed
30. Which of the following is the mathematical representation of law of conservation of total linear momentum?
a) dP/dt = 0
b) dF/dt = 0
c) dP/dt = Finternal
d) dF/dt = P
31. A ball of mass 2kg is moving with a speed of 10m/s along a flat surface. It collides with another ball of mass 3kg and comes to rest, what will be the speed of the second ball after collision?
a) The above said situation is not possible
32. Regarding the velocity of a particle in uniform circular motion about a fixed axis, select the correct option. w & r angular velocity and radius vectors respectively. ‘X’ & ‘ . ’ represent cross & dot products respectively.
a) v = r X w
b) v = w X r
c) v = w.r
d) w = v.r
33. Which of the following statements is false?
a) Cross product is commutative
b) Cross product is distributive over addition
c) Dot product of two vectors gives a scalar
d) Dot product is commutative
34. Find the vector product (a X b) of the two given vectors: a = 2i + 3j + 4k, b = 3i + 5j. Here, i, j & k are unit vectors along three mutually perpendicular axes.
a) -20i + 12j + k
b) 10i + 6j + 1/2k
c) 20i – 12j – k
d) 10i – 6j -1/2k
35. What is the moment of inertia of a rod about an axis passing through the centre and perpendicular to its central axis? Given that mass of rod is 1kg, length = 10cm.
36. The moment of inertia of a solid sphere is 10kgm2. What will be the moment of inertia of a very thin spherical shell of the same mass and radius as that of the solid sphere?
37. What is the ratio of moment of inertia of a ring to a disc? Given that both have masses in the ratio 2:1 & radii in the ratio 1:2 respectively.
38. Moment of inertia, of a spinning body about an axis, doesn’t depend on which of the following factors?
a) Distribution of mass around axis
b) Orientation of axis
d) Angular velocity
39. Two cylinders have the same mass and radius. One is hollow and the other is solid. Which one will have the greater moment of inertia about the central axis?
a) Hollow cylinder
b) Solid cylinder
c) Same for both
d) Depends on length of cylinder
40. A solid disc has a mass of 10kg and radius 1m. Find its radius of gyration.
41. The moment of inertia of a planar disc about a diameter is 8kgm2. What is the moment of inertia about an axis passing through its centre and perpendicular to the plane of disc?
42. Let I1 be the moment of inertia about the centre of mass of a thick asymmetrical body. Let I2 be the moment of inertia about an axis parallel to I1. The distance between the two axes is ‘a’ & the mass of the body is ‘m’. Find the relation between I1 & I2.
a) I2 = I1 – ma2
b) I1 = I2 – ma2
c) I2 = I1
d) Parallel axis theorem can’t be used for a thick asymmetrical body
43. What is the moment of inertia of a rod, of mass 1kg & length 6m, about an axis perpendicular to rod’s length and at a distance of 1.5m from one end?
44. The moment of inertia of a ring about a tangent is 4kgm2. What is the moment of inertia about an axis passing through the centre of the ring and perpendicular to its plane? Mass of the ring is 2kg & diameter is 2m.
45. The moment of inertia of a planar square about a planar axis parallel to one side is 10kgm2. What is the moment of inertia about a diagonal?
46. A planar body is lying in the xz plane. What is the relation between its moment of inertia along the x, y & z axes?
a) Iz = Ix + Iy
b) Ix = Ix + Iz
c) Iy = Ix + Iz
d) Iz = Ix = Iy
47. Perpendicular axis theorem can be applied for which of the following bodies?
a) Ring having radius R & negligible cross section
b) Disc of radius R and thickness t
c) Cylinder of radius R and height h
d) A cube of side ‘a’
48. Consider two perpendicular axis in the plane of a planar body, such that I1 = 2 I2. The moment of inertia about an axis perpendicular to the plane and passing through intersection of I1 & I2 is 9kgm2. Find the value of I1& I2.
a) I1 = 9kg m2, I2 = 4.5kgm2
b) I1 = 3kg m2, I2 = 6kg m2
c) I1 = 6kg m2, I2 = 3kg m2
d) I1 = 18kg m2, I2 = 9kg m2
49. A body is in pure rotational motion about an axis. Its angular acceleration is given by: a = 2t. What is the angular distance covered by the body from t=2s to t=3s? It starts from rest at t=0.
a) 19/3 rad
b) 0 rad
c) 2/3 rad
d) 5/3 rad
50. A circular disc is rotating about a central axis perpendicular to its diameter with a speed of 5rad/s. If a constant force of 2N is applied tangentially on it, in how much time will it come to a stop? Radius of disc = 1m & mass = 1kg.
51. A disc of radius 10cm is rotating about the central axis perpendicular to its plane. A force of 5N acts on it tangentially. The disc was initially at rest. Calculate the value of power supplied by the force when the disc has rotated by 30°.The mass of the disc is 2kg.
52. A rod is rotating about one end. If a force F1 acting on the other end produces a torque T & supplies power P, find the value of force F2 that will produce the same amount of power when it acts at the midpoint of the rod. Assume that all forces are perpendicular to the axis of rotation & axis of rod. The rod starts from rest.
a) = F1
b) > F1
c) < F1
d) No force acting at any other point will produce the same power
53. A rigid body is rotating about an axis. One force F1 acts on the body such that its vector passes through the axis of rotation. Another force F2 acts on it such that it is perpendicular to the axis of rotation and at a point 5cm from the axis. This force F2 is perpendicular to the radius vector at its point of application. Find the net torque on the body. Let F1 = 10N & F2= 5N.
54. A ring of radius 7cm is rotating about the central axis perpendicular to its plane. A force acts on it, tangentially, such that it does a work of 10J in a complete rotation. Find the value of that force. `
a) 0.5/7π N
b) 35π N
c) 500/7π N
d) 0.7 N
55. Which of the following quantities is zero if torque on a particle is zero?
a) Angular momentum of the particle
b) Angular speed of the particle
c) Change in kinetic energy of the particle
d) Rate of change of angular momentum
56. A particle of mass 5kg is rotating about an axis in a circle with a speed of 10m/s. What should be its radius so that the component of angular momentum about the axis is 5kgm2/s?
57. A disc is rotating with ω =10rad/s about a fixed central axis which is perpendicular to its plane. The disc has a mass =2kg & radius =10cm. A small particle of mass 100gm is put slowly on the disc’s outer circumference. There is sufficient friction between the disc and the particle. What will be the new angular velocity of the system?
a) 10 rad/s
b) 9.09 rad/s
c) 9.51 rad/s
d) Can’t conserve angular momentum because of friction
58. A ring and a disc having masses in the ratio 1:2 are made to rotate about their central axes. Both are acted upon by the same torque when they are at rest. Which one will have more angular velocity when torque has been removed from both after the same time? Both have the same radius.
c) Same for both
d) Depends on ratio of mass and radius
59. A particle is rotating about a fixed axis. The angular momentum of the particle about any point on the fixed axis is the same. True or False?
60. What is the rate of change of angular momentum?
d) Angular velocity