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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 m_{1} and m_{2} (m_{1} > m_{2}) 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 m_{2}

(b) the C.M. moves towards m_{1}

(c) the C.M. remains at rest

(d) C.M. moves at right angle to the line joining m_{1} and m_{2}

## 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\(\hat{i}\) + \(\hat{j}\) + 5\(\hat{k}\) acting at the point r = 7\(\hat{i}\) + 3\(\hat{j}\) + \(\hat{i}\) is

(a) 14\(\hat{i}\) – 38\(\hat{j}\) + 16\(\hat{k}\)

(b) 4\(\hat{i}\) + 4\(\hat{j}\) + 6\(\hat{k}\)

(c) -21\(\hat{i}\) + 4\(\hat{j}\) + 4\(\hat{k}\)

(d) -14\(\hat{i}\) + 38\(\hat{j}\) – 16\(\hat{k}\)

## Answer

Answer: (a) 14\(\hat{i}\) – 38\(\hat{j}\) + 16\(\hat{k}\)

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, v_{cm} = 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 \(\sqrt{\frac {7}{5}}\)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 m_{1} and m_{2} is given by m_{1}m_{2}/m_{1} + m_{2}.

(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 watch is equal to \(\frac {π}{60}\) 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 sails 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) \(\frac {m_1m_2}{m_1+m_2}\) | (ii) internal forces |

(c) \(\frac {r_1+r_2}{2}\) | (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) \(\frac {m_1m_2}{m_1+m_2}\) | (i) reduced mass of two particle system |

(c) \(\frac {r_1+r_2}{2}\) | (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) xF_{y} – yF_{x} |

(c) Average power (P) | (iii) Fd |

## Answer

Answer:

Column I | Column II |

(a) Torque perpendicular to the x-y plane | (ii) xF_{y} – yF_{x} |

(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 = I_{c} + mr² |

(b) Theorem of parallel axes | (ii) I_{x} = I_{x} + I_{y} |

(c) M.I. of a rod about an axis through its C.M. and ⊥ to its length | (iii) \(\frac {1}{2}\) mr² |

(d) M.I. of a circular ring about its diameter | (iv) \(\frac {1}{12}\) mL² |

## Answer

Answer:

Column I | Column II |

(a) Theorem of perpendicular axes | (ii) I_{x} = I_{x} + I_{y} |

(b) Theorem of parallel axes | (i) I = I_{c} + mr² |

(c) M.I. of a rod about an axis through its C.M. and ⊥ to its length | (iv) \(\frac {1}{12}\) mL² |

(d) M.I. of a circular ring about its diameter | (iii) \(\frac {1}{2}\) mr² |

Column I | Column II |

(a) M.I. of a solid sphere about its diameter | (i) \(\frac {1}{2}\) MR² |

(b) M.I. of a solid sphere about a tangent | (ii) \(\frac {1}{4}\) MR² |

(c) M.I. of a disc about its diameter | (iii) \(\frac {2}{5}\) MR² |

(d) M.I. of a cylinder about its axis of symmetry | (iv) \(\frac {7}{5}\) MR² |

## Answer

Answer:

Column I | Column II |

(a) M.I. of a solid sphere about its diameter | (iii) \(\frac {2}{5}\) MR² |

(b) M.I. of a solid sphere about a tangent | (iv) \(\frac {7}{5}\) MR² |

(c) M.I. of a disc about its diameter | (ii) \(\frac {1}{4}\) MR² |

(d) M.I. of a cylinder about its axis of symmetry | (i) \(\frac {1}{2}\) MR² |

Object | K²/R² |

(a) Ring | (i) \(\frac {2}{5}\) |

(b) Disc | (ii) 1 |

(c) Solid sphere | (iii) \(\frac {1}{2}\) |

## Answer

Answer:

Object | K²/R² |

(a) Ring | (ii) 1 |

(b) Disc | (iii) \(\frac {1}{2}\) |

(c) Solid sphere | (i) \(\frac {2}{5}\) |

Object | K²/R² |

(a) Hollow sphere | (i) 1 |

(b) Solid cylinder | (ii) \(\frac {2}{3}\) |

(c) Hollow cylinder | (iii) \(\frac {1}{2}\) |

## Answer

Answer:

Object | K²/R² |

(a) Hollow sphere | (ii) \(\frac {2}{3}\) |

(b) Solid cylinder | (iii) \(\frac {1}{2}\) |

(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) µ_{s} = \(\frac {1}{3}\) θ |

(e) Acceleration produced in a body on an inclined plane | (v) a = \(\frac {g sin θ}{M+\frac{1}{R^2}}\) |

## 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) µ_{s} = \(\frac {1}{3}\) θ |

(d) Acceleration produced in a body rolling without slipping | (v) a = \(\frac {g sin θ}{M+\frac{1}{R^2}}\) |

(e) Acceleration produced in a body on an inclined plane | (iii) a = g sin θ |

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