Class 11 Exam > Class 11 Questions > Out of the following pairs, which one does no...
Start Learning for Free
Out of the following pairs, which one does not have identical dimensions ?
[AIEEE 2005]
- a)Angular momentum and Planck's constant
- b)Impulse and momentum
- c)Moment of inertia and moment of a force
- d)Work and torque
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Out of the following pairs, which one does not have identical dimensio...
I = mr2
∴[I] = [ML2]
and
= moment of force = 
∴
= [L][MLT-2]=[ML2T-2]
∴[I] = [ML2]
and
= moment of force = ∴
= [L][MLT-2]=[ML2T-2]Most Upvoted Answer
Out of the following pairs, which one does not have identical dimensio...
Explanation:
• Dimension is defined as the power to which fundamental quantities are raised to express the physical quantity.
• The fundamental quantities are mass, length, and time.
• The dimensions of all physical quantities can be expressed in terms of these fundamental quantities.
a) Angular momentum and Planck's constant:
• Angular momentum is the product of moment of inertia and angular velocity.
• Moment of inertia has dimensions of mass × length² and angular velocity has dimensions of length/time.
• Hence, the dimensions of angular momentum are (mass × length²) × (length/time) = mass × length²/time.
• Planck's constant has dimensions of energy × time.
• Hence, the dimensions of angular momentum and Planck's constant are not the same.
b) Impulse and momentum:
• Impulse is the product of force and time, and momentum is the product of mass and velocity.
• Force has dimensions of mass × length/time², time has dimensions of time, mass has dimensions of mass, and velocity has dimensions of length/time.
• Hence, the dimensions of impulse are (mass × length/time²) × time = mass × length/time.
• The dimensions of momentum are mass × (length/time).
• Therefore, the dimensions of impulse and momentum are the same.
c) Moment of inertia and moment of a force:
• Moment of inertia is the product of mass and the square of the distance from the axis of rotation.
• The dimensions of mass are mass, and the dimensions of distance are length.
• Hence, the dimensions of moment of inertia are mass × length².
• Moment of a force is the product of force and distance.
• The dimensions of force are mass × length/time², and the dimensions of distance are length.
• Hence, the dimensions of moment of a force are (mass × length/time²) × length = mass × length²/time².
• Therefore, the dimensions of moment of inertia and moment of a force are not the same.
d) Work and torque:
• Work is the product of force and displacement, and torque is the product of force and the perpendicular distance from the axis of rotation.
• The dimensions of force are mass × length/time², the dimensions of displacement are length, and the dimensions of distance are length.
• Hence, the dimensions of work are (mass × length/time²) × length = mass × length²/time².
• The dimensions of torque are (mass × length/time²) × length = mass × length²/time².
• Therefore, the dimensions of work and torque are the same.
Hence, the correct answer is option C, i.e., moment of inertia and moment of a force do not have identical dimensions.
• Dimension is defined as the power to which fundamental quantities are raised to express the physical quantity.
• The fundamental quantities are mass, length, and time.
• The dimensions of all physical quantities can be expressed in terms of these fundamental quantities.
a) Angular momentum and Planck's constant:
• Angular momentum is the product of moment of inertia and angular velocity.
• Moment of inertia has dimensions of mass × length² and angular velocity has dimensions of length/time.
• Hence, the dimensions of angular momentum are (mass × length²) × (length/time) = mass × length²/time.
• Planck's constant has dimensions of energy × time.
• Hence, the dimensions of angular momentum and Planck's constant are not the same.
b) Impulse and momentum:
• Impulse is the product of force and time, and momentum is the product of mass and velocity.
• Force has dimensions of mass × length/time², time has dimensions of time, mass has dimensions of mass, and velocity has dimensions of length/time.
• Hence, the dimensions of impulse are (mass × length/time²) × time = mass × length/time.
• The dimensions of momentum are mass × (length/time).
• Therefore, the dimensions of impulse and momentum are the same.
c) Moment of inertia and moment of a force:
• Moment of inertia is the product of mass and the square of the distance from the axis of rotation.
• The dimensions of mass are mass, and the dimensions of distance are length.
• Hence, the dimensions of moment of inertia are mass × length².
• Moment of a force is the product of force and distance.
• The dimensions of force are mass × length/time², and the dimensions of distance are length.
• Hence, the dimensions of moment of a force are (mass × length/time²) × length = mass × length²/time².
• Therefore, the dimensions of moment of inertia and moment of a force are not the same.
d) Work and torque:
• Work is the product of force and displacement, and torque is the product of force and the perpendicular distance from the axis of rotation.
• The dimensions of force are mass × length/time², the dimensions of displacement are length, and the dimensions of distance are length.
• Hence, the dimensions of work are (mass × length/time²) × length = mass × length²/time².
• The dimensions of torque are (mass × length/time²) × length = mass × length²/time².
• Therefore, the dimensions of work and torque are the same.
Hence, the correct answer is option C, i.e., moment of inertia and moment of a force do not have identical dimensions.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
Out of the following pairs, which one does not have identical dimensions ?[AIEEE 2005]a)Angular momentum and Plancks constantb)Impulse and momentumc)Moment of inertia and moment of a forced)Work and torqueCorrect answer is option 'C'. Can you explain this answer?
Question Description
Out of the following pairs, which one does not have identical dimensions ?[AIEEE 2005]a)Angular momentum and Plancks constantb)Impulse and momentumc)Moment of inertia and moment of a forced)Work and torqueCorrect answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Out of the following pairs, which one does not have identical dimensions ?[AIEEE 2005]a)Angular momentum and Plancks constantb)Impulse and momentumc)Moment of inertia and moment of a forced)Work and torqueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Out of the following pairs, which one does not have identical dimensions ?[AIEEE 2005]a)Angular momentum and Plancks constantb)Impulse and momentumc)Moment of inertia and moment of a forced)Work and torqueCorrect answer is option 'C'. Can you explain this answer?.
Out of the following pairs, which one does not have identical dimensions ?[AIEEE 2005]a)Angular momentum and Plancks constantb)Impulse and momentumc)Moment of inertia and moment of a forced)Work and torqueCorrect answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Out of the following pairs, which one does not have identical dimensions ?[AIEEE 2005]a)Angular momentum and Plancks constantb)Impulse and momentumc)Moment of inertia and moment of a forced)Work and torqueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Out of the following pairs, which one does not have identical dimensions ?[AIEEE 2005]a)Angular momentum and Plancks constantb)Impulse and momentumc)Moment of inertia and moment of a forced)Work and torqueCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Out of the following pairs, which one does not have identical dimensions ?[AIEEE 2005]a)Angular momentum and Plancks constantb)Impulse and momentumc)Moment of inertia and moment of a forced)Work and torqueCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of Out of the following pairs, which one does not have identical dimensions ?[AIEEE 2005]a)Angular momentum and Plancks constantb)Impulse and momentumc)Moment of inertia and moment of a forced)Work and torqueCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Out of the following pairs, which one does not have identical dimensions ?[AIEEE 2005]a)Angular momentum and Plancks constantb)Impulse and momentumc)Moment of inertia and moment of a forced)Work and torqueCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Out of the following pairs, which one does not have identical dimensions ?[AIEEE 2005]a)Angular momentum and Plancks constantb)Impulse and momentumc)Moment of inertia and moment of a forced)Work and torqueCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Out of the following pairs, which one does not have identical dimensions ?[AIEEE 2005]a)Angular momentum and Plancks constantb)Impulse and momentumc)Moment of inertia and moment of a forced)Work and torqueCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Out of the following pairs, which one does not have identical dimensions ?[AIEEE 2005]a)Angular momentum and Plancks constantb)Impulse and momentumc)Moment of inertia and moment of a forced)Work and torqueCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup