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System of Particles and Rotational Motion Class 11 MCQs Questions with Answers
Multiple Choice Type Questions
Question 1.
Three identical balls each of radius 10cm and mass 1kg each are placed touching each other on a horizontal surface. Where is their C.M. located?
(a) At the centre of one ball.
(b) On the horizontal surface.
(c) At the point of contact of any two spheres.
(d) None of these.
Answer
Answer: (b) On the horizontal surface.
Question 2.
A body rolls without slipping. The radius of gyration of the body about an axis passing through its centre of mass is K. If radius of the body be R, then what is the ratio of its rational K.E. to translational K.E.?
(a) (frac K^2 R^2)
(b) (frac K^2 R^2) + R²
(c) (frac R^2 K^2) + R²
(d) K² + R^2
Answer
Answer: (a) (frac K^2 R^2)
Question 3.
A body is under the action of two equal and oppositely directed forces and the body is rotating with constant acceleration. Which of the following cannot be the separation between the lines of action of the forces?
(a) zero
(b) 0.25m
(c) 0.4m
(d) 1.0m
Answer
Answer: (a) zero
Question 4.
A body of mass M slides down an inclined plane and reaches the bottom with velocity v. If a ring of same mass rolls down the same inclined plane, what will be its velocity on reaching the bottom?
(a) (frac v 2)
(b) (frac v √2)
(c) v
(d) √2v
Answer
Answer: (b) (frac v √2)
Question 5.
A ring of radius R slides down an inclined plane and reaches the bottom with speed v. If the radius of the ring is doubled keeping its M.I. constant, the speed at the bottom of the inclined plane will be
(a) v
(b) 2v
(c) √2v
(d) (frac v √2)
Answer
Answer: (a) v
Question 6.
A uniform rod of length l is rotating horizontally with uniform angular speed co about a vertical axis passing through its one end. The force exerted on the rod is
(a) mlω²
(b) ml²ω²
(c) (frac 1 2) ml²ω²
(d) (frac 1 2) mlω
Answer
Answer: (d) (frac 1 2) mlω
Question 7.
The pendulum consists of a sphere of mass m suspended with a flexible wire of length l. If the breaking strength of the wire is 2mg, then the angular displacement that can be given to the pendulum is
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer
Answer: (c) 60°
Question 8.
A string of length l fixed at one end carries a mass M at the other end. The string makes (frac 2 π) revolutions per second around a vertical axis through the fixed end. The tension in the string is
(d) Ml
(b) 2Ml
(d) 4Ml
(d) 16Ml
Answer
Answer: (d) 16Ml
Question 9.
A wheel has radius 10cm and is coupled by a belt to another wheel of radius 30cm. The smaller wheel increases its speed from rest at a uniform rate of π rads-2. The speed of larger wheel become 100 rpm after
(a) 2s
(b) 5s
(c) 20s
(d) 10s
Answer
Answer: (d) 10s
Question 10.
Three thin iron rods each of mass M and length l are welded so as to form an equilateral triangle. The M.I. about the axis passing through the C.M. and perpendicular to its plane is
(a) Ml²
(b) (frac Ml^2 3 )
(c) (frac Ml^2 2)
(d) (frac Ml^2 4)
Answer
Answer: (c) (frac Ml^2 2)
Question 11.
If the rods in Q.10 are joined to form letter H, thenM.I. of the system about one of sides of H will be
(a) (frac Ml^2 3 )
(b) (frac Ml^2 4 )
(c) 2(frac Ml^2 3 )
(d) (frac 4 3 ) Ml²
Answer
Answer: (d) (frac 4 3 ) Ml²
Question 12.
In Q. 11, M.I. about side joining the outer sides will be
(a) (frac Ml^2 6 )
(b) (frac Ml^2 4 )
(c) 2(frac 2Ml^2 3 )
(d) (frac Ml^2 12 )
Answer
Answer: (a) (frac Ml^2 6 )
Question 13.
When a torque acting on a system is zero, then which of the following should not change?
(a) Linear velocity
(b) Angular momentum
(c) Angular displacement
(d) Force acting on the body
Answer
Answer: (b) Angular momentum
Question 14.
The moment of inertia of a body does not depend upon
(a) the mass of the body
(b) the axis of rotation of the body
(c) the distribution of the mass in the body
(d) the angular velocity of the body
Answer
Answer: (d) the angular velocity of the body
Question 15.
Two particles pf masses m1 and m2 (m1 > m2) attract each other with a force inversely proportional to the square of the distance between them. The particles are initially held at rest and then released. Then
(a) the C.M. moves towards m2
(b) the C.M. moves towards m1
(c) the C.M. remains at rest
(d) C.M. moves at right angle to the line joining m1 and m2
Answer
Answer: (c) the C.M. remains at rest
Question 16.
Without weighing how will you distinguish between the two identical balls of same material, but one being solid and the other being hollow
(a) by spinning them by equal torque.
(b) by rolling them down an inclined plane in air.
(c) by determining their M.I. about the centre.
(d) all of the above.
Answer
Answer: (d) all of the above.
Question 17.
The torque of a force F = -3(hati) + (hatj) + 5(hatk) acting at the point r = 7(hati) + 3(hatj) + (hati) is
(a) 14(hati) – 38(hatj) + 16(hatk)
(b) 4(hati) + 4(hatj) + 6(hatk)
(c) -21(hati) + 4(hatj) + 4(hatk)
(d) -14(hati) + 38(hatj) – 16(hatk)
Answer
Answer: (a) 14(hati) – 38(hatj) + 16(hatk)
Question 18.
A thin ring of mass M and radius r is rotating about its axis with a constant angular velocity ω. Two particles each of mass m are placed gently to the opposite ends of the diameter of the ring. The new angular velocity of the ring will be
(a) (frac ωM M+m )
(b) (frac ω(M-2m) M+2m )
(c) 2(frac ω(M+2m) M )
(d) (frac ωM M+2m )
Answer
Answer: (d) (frac ωM M+2m )
Question 19.
Two rings have their moments of inertia in the ratio 2 : 1 and their diameters are in the ratio 2 : 1. The ratio of their masses will be
(a) 2 : 1
(b) 1 : 2
(c) 1 : 4
(d) 1 : 1
Answer
Answer: (b) 1 : 2
Question 20.
When a dish containing mercury and water is rotated about a vertical axis, the outer portion of the dish contains :
(a) Water
(b) Mercury
(c) Mixture of water and mercury
(d) Nothing
Answer
Answer: (b) Mercury
Fill in the blanks
Question 1.
The C.M. is that point about which the vector sum of the ……………… of individual particles of the body becomes zero.
Answer
Answer: mass moments
Question 2.
If a hollow cylinder is half filled with water, then its C.G. will move ……………….
Answer
Answer: downward
Question 3.
If a body in unstable equilibrium is disturbed slightly, its C.G. is …………….
Answer
Answer: lowered
Question 4.
The point at which whole weight of the body is concentrated is called …………..
Answer
Answer: centre of gravity
Question 5.
If a body is at rest i.e, vcm = 0 and angular speed ω = 0, then the body is said to be in ……………… equilibrium.
Answer
Answer: static
Question 6.
Angular acceleration is produced in a body when a ……………… acts on it.
Answer
Answer: torque
Question 7.
…………….. is the example of a body in which C.M. lies outside.
Answer
Answer: Ring
Question 8.
……………… of momentum is called angular momentum.
Answer
Answer: Moment
Question 9.
…………….. is called as the root mean square distance at which whole mass of the body is supposed to be concentrated.
Answer
Answer: Radius of gyration
Question 10.
A ……………. shows all the forces applied on a body by all other bodies.
Answer
Answer: free body diagram
Question 11.
………………. plays the same role in rotatory motion as is being played by the mass in the translational motion.
Answer
Answer: Moment of inertia
True/False Type Questions
1. Which of the following statements are True/False?
(a) Moment of inertia in rotational motion is analogue of mass in translational motion.
(b) C.M. of a circular disc lies ouitside the material of the body.
(c) C.G. and C.M. coincide for homogeneous mass distribution.
(d) Sum of moments of masses of a system about the C.M. is always zero.
Answer
Answer:
(a) True
(b) False
(c) True
(d) True
2. Tell which one is True/False out of the following
(a) Reduced mass concept is very useful in the study of motion of two particle system.
(b) For complete equilibrium, the body should have neither translatory motion nor rotatory motion.
(c) The direction of angular acceleration is tangential to a circle in which a mass is revolving.
(d) The angular acceleration of a body rotating with a uniform angular velocity is always zero.
Answer
Answer:
(a) True
(b) True
(c) True
(d) True
3. Tell which of the following statements are True/False?
(a) It becomes easier to open or close a door if the force is applied at the free edge of the door.
(b) Torque is the rotational analogue of force in linear motion.
(c) The moment of momentum is called angular momentum.
(d) When a mass is rotating in a plane about a fixed point, then its angular momentum is directed along the axis of rotation.
Answer
Answer:
(a) True
(b) True
(c) True
(d) True
4. Tell which of the following statements are True/False?
(a) A mass M is moving with a constant velocity parallel to X-axis. Its angular momentum w.r.t. origin remains constant.
(b) A dancer on ice spins faster when she folds her arms. It is due to decrease in her M.I.
(c) M.I. does not change with the change of the axis of rotation.
(d) Radius gyration of a body is a constant quantity.
Answer
Answer:
(a) True
(b) True
(c) False
(d) False
5. Which of the following statements is True/False?
The rotational energy of a body with a given angular speed depends on its
(a) mass only
(b) material only
(c) size only
(d) mass as well as the distribution of its mass about the axis of rotation.
Answer
Answer:
(a) False
(b) False
(c) False
(d) True
6. Tell which one of the following statement is True/False?
(a) A swimmer while jumping into water from a height easily forms a loop in air if he pulls his arms and legs in.
(b) M.I. of a body depends upon its angular velocity.
(c) The radius of gyration of a solid sphere about a tangent is (sqrtfrac 75)R
(d) M.I. of a solid cylinder about the line of contact is MR².
Answer
Answer:
(a) True
(b) False
(c) True
(d) False
7. Tell which of the following statements are True/False?
(a) C.M. moves with a constant velocity in the absence of an external force.
(b) The C.M. of a body should necessarily lie on the body.
(c) A system of particles interacting with each other has only K.E.
(d) A body have momentum without energy.
Answer
Answer:
(a) True
(b) False
(c) False
(d) False
8. Which of the following is True/False?
(a) There may be no mass at the C.M. of a system.
(b) If the torque is not zero, the rotational equilibrium will not be there.
(c) M.I. of a solid cylinder about its axis depends upon its length.
(d) If r and F lie in the same plane, then X will not have any component in that plane.
Answer
Answer:
(a) True
(b) True
(c) False
(d) True
9. Which of the following is True/False?
(a) Only an external force can change the state of motion of the C.M. of the body.
(b) The reduced mass of two particles of mass m1 and m2 is given by m1m2/m1 + m2.
(c) If a body in unstable equilibrium is disturbed slightly, its C.G. is lowered.
Answer
Answer:
(a) True
(b) True
(c) True
10. Which of the following statements are True/False?
(a) The angular speed of the top of the second hand of a stream is equal to (frac π60) rads-1.
(b) In a rotational motion, the direction of the force and its distance from the point of rotation are equally important.
(c) A sail boat can be propelled by air blown at its saeakhabaar from a fan fixed to the boat.
(d) A body cannot have momentum without energy.
Answer
Answer:
(a) False
(b) True
(c) False
(d) True
Match Type Questions
| Column I | Column II |
| (a) Always appear in pairs | (i) reduced mass of two particle system |
| (b) (frac m_1m_2m_1+m_2) | (ii) internal forces |
| (c) (frac r_1+r_22) | (iii) position vector of C.M. of two particles of equal masses |
Answer
Answer:
| Column I | Column II |
| (a) Always appear in pairs | (ii) internal forces |
| (b) (frac m_1m_2m_1+m_2) | (i) reduced mass of two particle system |
| (c) (frac r_1+r_22) | (iii) position vector of C.M. of two particles of equal masses |
| Column I | Column II |
| (a) Torque perpendicular to the x-y plane | (i) τω |
| (b) Torque in terms of lever arm | (ii) xFy – yFx |
| (c) Average power (P) | (iii) Fd |
Answer
Answer:
| Column I | Column II |
| (a) Torque perpendicular to the x-y plane | (ii) xFy – yFx |
| (b) Torque in terms of lever arm | (iii) Fd |
| (c) Average power (P) | (i) τω |
| Column I | Column II |
| (a) Radial component of force | (i) pd |
| (b) Transverse component of force | (ii) F cos ø |
| (c) Angular momentum | (iii) F sin ø |
Answer
Answer:
| Column I | Column II |
| (a) Radial component of force | (ii) F cos ø |
| (b) Transverse component of force | (iii) F sin ø |
| (c) Angular momentum | (i) pd |
| Column I | Column II |
| (a) S.I. unit of M.I. | (i) Nm |
| (b) S.I. unit of torque | (ii) m |
| (c) S.I. unit of angular momentum | (iii) kgm²s-1 |
| (d) S.I. unit of radius of gyration | (iv) kgm² |
Answer
Answer:
| Column I | Column II |
| (a) S.I. unit of M.I. | (iv) kgm² |
| (b) S.I. unit of torque | (i) Nm |
| (c) S.I. unit of angular momentum | (iii) kgm²s-1 |
| (d) S.I. unit of radius of gyration | (ii) m |
| Column I | Column II |
| (a) A body whose particles remain at their respective positions during its rotational or translational motion | (i) moment of inertia |
| (b) r.m.s. distance of constituting particles from the axis of rotation | (ii) rigid body |
| (c) Sum of products of the masses of the constituent particles and square of their normal distance from the axis of rotation | (iii) radius of gyration |
Answer
Answer:
| Column I | Column II |
| (a) A body whose particles remain at their respective positions during its rotational or translational motion | (ii) rigid body |
| (b) r.m.s. distance of constituting particles from the axis of rotation | (iii) radius of gyration |
| (c) Sum of products of the masses of the constituent particles and square of their normal distance from the axis of rotation | (i) moment of inertia |
| Column I | Column II |
| (a) Theorem of perpendicular axes | (i) I = Ic + mr² |
| (b) Theorem of parallel axes | (ii) Ix = Ix + Iy |
| (c) M.I. of a rod about an axis through its C.M. and ⊥ to its length | (iii) (frac 12) mr² |
| (d) M.I. of a circular ring about its diameter | (iv) (frac 112) mL² |
Answer
Answer:
| Column I | Column II |
| (a) Theorem of perpendicular axes | (ii) Ix = Ix + Iy |
| (b) Theorem of parallel axes | (i) I = Ic + mr² |
| (c) M.I. of a rod about an axis through its C.M. and ⊥ to its length | (iv) (frac 112) mL² |
| (d) M.I. of a circular ring about its diameter | (iii) (frac 12) mr² |
| Column I | Column II |
| (a) M.I. of a solid sphere about its diameter | (i) (frac 12) MR² |
| (b) M.I. of a solid sphere about a tangent | (ii) (frac 14) MR² |
| (c) M.I. of a disc about its diameter | (iii) (frac 25) MR² |
| (d) M.I. of a cylinder about its axis of symmetry | (iv) (frac 75) MR² |
Answer
Answer:
| Column I | Column II |
| (a) M.I. of a solid sphere about its diameter | (iii) (frac 25) MR² |
| (b) M.I. of a solid sphere about a tangent | (iv) (frac 75) MR² |
| (c) M.I. of a disc about its diameter | (ii) (frac 14) MR² |
| (d) M.I. of a cylinder about its axis of symmetry | (i) (frac 12) MR² |
| Object | K²/R² |
| (a) Ring | (i) (frac 25) |
| (b) Disc | (ii) 1 |
| (c) Solid sphere | (iii) (frac 12) |
Answer
Answer:
| Object | K²/R² |
| (a) Ring | (ii) 1 |
| (b) Disc | (iii) (frac 12) |
| (c) Solid sphere | (i) (frac 25) |
| Object | K²/R² |
| (a) Hollow sphere | (i) 1 |
| (b) Solid cylinder | (ii) (frac 23) |
| (c) Hollow cylinder | (iii) (frac 12) |
Answer
Answer:
| Object | K²/R² |
| (a) Hollow sphere | (ii) (frac 23) |
| (b) Solid cylinder | (iii) (frac 12) |
| (c) Hollow cylinder | (i) 1 |
| Column I | Column II |
| (a) Tension in the string provides the torque | (i) Motion of a cylinder rolling without slipping on an inclined plane |
| (b) Friction contributes to the torque | (ii) Motion of a point mass tied to a string wound on the cylinder |
| (c) Condition for rolling without slipping | (iii) a = g sin θ |
| (d) Acceleration produced in a body rolling without slipping | (iv) µs = (frac 13) θ |
| (e) Acceleration produced in a body on an inclined plane | (v) a = (frac g sin θM+frac1R^2) |
Answer
Answer:
| Column I | Column II |
| (a) Tension in the string provides the torque | (ii) Motion of a point mass tied to a string wound on the cylinder |
| (b) Friction contributes to the torque | (i) Motion of a cylinder rolling without slipping on an inclined plane |
| (c) Condition for rolling without slipping | (iv) µs = (frac 13) θ |
| (d) Acceleration produced in a body rolling without slipping | (v) a = (frac g sin θM+frac1R^2) |
| (e) Acceleration produced in a body on an inclined plane | (iii) a = g sin θ |
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