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In this chapter, the role of Newton's laws of motion is emphasized, which are applied to both linear and rotational systems. For example, consider operating a motor vehicle. The car's wheels (rotational bodies) turn when you steer because you are exerting torque on the steering wheel.
NCERT Exemplar Class 11 Physics Solutions, offers thorough explanations of particle behavior and rotational motion. This chapter's solutions help students in understanding key concepts that are essential to learn the motion of extended objects, such as the center of mass and moment of inertia.
Through the NCERT Exemplar Class 11 Physics Chapter 7 solutions, students can improve their understanding of how particles move in systems and how forces lead to rotational motion.
NCERT Exemplar solutions for class 11 Physics chapter 7 System of Particles and Rotational, is exclusively prepared only by experts. These solutions help students to prepare for competitive exams like JEE Main and NEET.
Question:7.1
For which of the following does the centre of mass lie outside the body?
(a) A pencil
(b) A shotput
(c) A dice
(d) A bangle
Answer:
The answer is the option (d) A Bangle.Question:7.2
Which of the following points is the likely position of the center of mass of the system shown in Fig. 7.1?
(a) A
(b) B
(c) C
(d) D
Answer:
The answer is the option (c) CQuestion:7.3
Answer:
The answer is the option (b). Angular momentum of an object is given byQuestion:7.4
When a disc rotates with uniform angular velocity, which of the following is not true?
(a) The sense of rotation remains same.
(b) The orientation of the axis of rotation remains same.
(c) The speed of rotation is non-zero and remains same.
(d) The angular acceleration is non-zero and remains same.
Answer:
The answer is the option (d)Question:7.5
A uniform square plate has a small piece Q of an irregular shape removed and glued to the centre of the plate leaving a hole behind (Fig. 7.3). The moment of inertia about the z-axis is then
(a) increased
(b) decreased
(c) the same
(d) changed in unpredicted manner.
Answer:
The answer is the option (b) The formula for Moment of Inertia is given byQuestion:7.6
In problem 7.5. the CM of the plate is now in the following quadrant of x-y plane
a) I
b) II
c) III
d) IV
Answer:
The answer is the option (c) III. The centre of mass will shift towards the side opposite to Q along the line passing through the axis of rotation. Thus, the new centre of mass will be in quadrant III. Hence, C is the answer.Question:7.7
Answer:
The correct answer is the optionQuestion:7.8
Answer:
The correct answer is the optionQuestion:7.9
Choose the correct alternatives:
(a) For a general rotational motion, angular momentum L and angular velocity
(b) For a rotational motion about a fixed axis, angular momentum L and angular velocity
(c) For a general translational motion , momentum p and velocity v are always parallel.
(d) For a general translational motion, acceleration a and velocity v are always parallel.
Answer:
The correct answer is the option (a) and (c).Question:7.10
Figure 7.4 shows two identical particles 1 and 2, each of mass m, moving in opposite directions with same speed v along parallel lines.
At a particular instant,
(a) Angular momentum
(b) Angular momentum
(c) Total angular momentum of the system about A is
(d) Total angular momentum of the system about A is
Answer:
The correct answer is the option (a) and (d)Question:7.11
The net external torque on a system of particle about an axis is zero. Which of the following are compatible with it?
a) the forces may be acting radially from a point on the axis
b) the forces may be acting on the axis of rotation
c) the forces may be acting parallel to the axis of rotation
d) the torque caused by some forces may be equal and opposite to that caused by other forces
Answer:
The correct answer is the option (a, b, c, d) Torque is given byQuestion:7.12
Figure 7.5 shows a lamina in x-y plane. Two axes z and z′ pass perpendicular to its plane. A force F acts in the plane of lamina at point P as shown. Which of the following are true? (The point P is closer to z′-axis than the z-axis.)
(a) Torque
(b) Torque
(c) Torque
(d) Total torque is given be
Answer:
The correct answer is the option (b) and (c)Question:7.13
With reference to Fig. 7.6 of a cube of edge a and mass m, state whether the following are true or false. (O is the centre of the cube.)
(a) The moment of inertia of cube about z-axis is
(b) The moment of inertia of cube about z' is
(c) The moment of inertia of cube about z'' is
(d)
Answer:
The correct answer is the option (a), (b), and (d).So b is correct
Since Z-axis and z" axis are not parallel to each other, so parallel theorem is not applicable here, rendering option c wrong
Since Z axis passes through the centre of the cube, so x and y-axis are symmetric
Hence, d is correct
Question:7.14
Answer:
An object is called small if it is the vertical height or geometric centre lies remarkably close to the earth surface. According to this concept, a building and a pond are smaller objects with their geometrical centres remarkably close to the earth surface. Whereas mountain and lake are extended objects as their geometrical centres are above and below the surface of the earth, respectively.Question:7.15
Answer:
Moment of Inertia is given byQuestion:7.16
Answer:
Question:7.17
Uniform cube of mass m and side a is placed in a frictionless horizontal surface. A vertical force F is applied to the edge as shown in the figure.
Match the following
a)
|
i) cube will move up
|
b)
|
ii) cube will not exhibit motion
|
c)
|
iii) cube will begin to rotate and slip at A
|
d)
|
iv)normal reaction effectively at
|
Answer:
(a) – (ii), (b) – (iii), (c) – (i), (d) – (iv)Question:7.18
A uniform sphere of mass m and radius R is placed on a rough horizontal surface. The sphere is struck horizontally at a height h from the floor.
Match the following
a)
|
i) sphere rolls without slipping with a constant velocity and no loss of energy
|
b)
|
ii) sphere spins clockwise, loses energy by friction
|
c)
|
iii) sphere spins anti-clockwise, loses energy by friction
|
d)
|
iv) sphere has only a translational motion, loses energy by friction
|
Answer:
(a)-(iii), (c)-(ii), (d) -(i), (b)-(iv)Question:7.19
Answer:
The vector sum of all torques due to forces at a point is 0. Let us assume thatQuestion:7.20
Answer:
The wheel is a rigid elastic body. When a wheel is in uniform motion about the axis passing through its centre and perpendicular to the plane of the wheel, every particle of the wheel is also in a circular motion about the above axis. The centripetal acceleration acting on each particle is directed towards the axis of rotation due to elastic forces which are in pairs.Question:7.21
Answer:
InQuestion:7.22
Answer:
The centre of mass of a regular polygon with n sides lies on its geometric centre. If mass m is placed at all the n vertices, then the C.O.M is again at the geometric centre. LetQuestion:7.23
Find the centre of mass of a uniform
a) half-disc
b) quarter-disc
Answer:
Let the mass of half-disc be MQuestion:7.24
Answer:
(a) The law of conservation of angular momentum is applicable to this situation because there is no net external torque acting on the system. Gravitational and its normal reaction cancel out each other thus resulting in a 0 net torque.Question:7.25
Answer:
(a) Before coming in contact with the table, the disc was undergoing only rotational motion about its axis that passes through the centre. The velocity of C.O.M =0 since the point on the axis is considered at restQuestion:7.26
Answer:
Question:7.27
Answer:
Question:7.28
Answer:
Rigid Bodies and Their Properties
Understand how rigid bodies maintain their shape and resist changes in position when forces are applied.
Fixed Axis of Rotation
Learn about the concept of a fixed axis, where a rigid body rotates around a stationary point.
Newton’s Laws of Motion for Particles
Study the application of Newton's second and third laws to particles, with practical examples to illustrate their effects.
System of Particles and Rotational Motion
Explore the motion of systems with multiple particles and how rotational dynamics come into play.
Key Concepts: Vector, Center of Mass, and Angular Momentum
Grasp the significance of vectors, the center of mass, and angular momentum in analyzing particle and rotational motion.
Kinematic and Dynamic Aspects
Understand both kinematic (describing motion) and dynamic (explaining the causes of motion) perspectives in rotational motion.
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These important topics will help students build a solid foundation in rotational dynamics and the motion of extended objects.
Students will gain knowledge of rigid bodies and how they hold their place in the presence of applied external forces. Additionally discussed is the idea of a fixed axis, in which the rigid body stays stationary in a particular orientation. With the help of several real-world examples, the chapter discusses Newton's second and third laws of motion in relation to rigid bodies.
Chapter 1 | Units and Measurement |
Chapter 2 | Motion in a straight line |
Chapter 3 | Motion in a Plane |
Chapter 4 | Laws of Motion |
Chapter 5 | Work, Energy and Power |
Chapter 6 | System of Particles and Rotational motion |
Chapter 7 | Gravitation |
Chapter 8 | Mechanical Properties of Solids |
Chapter 9 | Mechanical Properties of Fluids |
Chapter 10 | Thermal Properties of Matter |
Chapter 11 | Thermodynamics |
Chapter 12 | Kinetic Theory |
Chapter 13 | Oscillations |
Chapter 14 | Waves |
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