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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?
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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.
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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?
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