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Out of the following pairs one which does not have identical dimensions is
- a)Moment of inertia and moment of a force
- b)Work and torque
- c)Angular momentum and planck's constant
- d)Impulse and momentum
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Out of the following pairs one which does not have identical dimensio...
Moment of inertia (I) = mr2
∴ [I] = [ML2]
Moment of force (τ) = rF
[τ] = [ML2T−2]
Moment of inertia and moment of a force do not have identical dimensions.
For work,
Hence, work and torque will have same dimensions.
Dimension of angular momentum is
Planck's constant is given as
Thus, Planck's constant and angular momentum have same dimension.
We know that impulse is defined as change in momentum, hence, they must have same dimension.
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Out of the following pairs one which does not have identical dimensio...
Explanation:
The moment of inertia and moment of force are two different physical quantities that do not have identical dimensions. We can understand this by looking at the units in which they are measured.
- Moment of inertia: Moment of inertia is a measure of an object's resistance to rotational motion. It is defined as the sum of the products of the masses of each particle in a body and the square of its distance from the axis of rotation. The moment of inertia is measured in kg.m2.
- Moment of force: Moment of force is a measure of the rotational effect of a force about a given point. It is defined as the product of the force and the perpendicular distance from the point to the line of action of the force. The moment of force is measured in N.m.
As we can see, the moment of inertia is measured in units of mass times distance squared, while the moment of force is measured in units of force times distance. These two quantities have different dimensions and cannot be considered identical.
Therefore, option A is the correct answer. Work and torque, angular momentum and Planck's constant, and impulse and momentum are all pairs of physical quantities that have identical dimensions.
The moment of inertia and moment of force are two different physical quantities that do not have identical dimensions. We can understand this by looking at the units in which they are measured.
- Moment of inertia: Moment of inertia is a measure of an object's resistance to rotational motion. It is defined as the sum of the products of the masses of each particle in a body and the square of its distance from the axis of rotation. The moment of inertia is measured in kg.m2.
- Moment of force: Moment of force is a measure of the rotational effect of a force about a given point. It is defined as the product of the force and the perpendicular distance from the point to the line of action of the force. The moment of force is measured in N.m.
As we can see, the moment of inertia is measured in units of mass times distance squared, while the moment of force is measured in units of force times distance. These two quantities have different dimensions and cannot be considered identical.
Therefore, option A is the correct answer. Work and torque, angular momentum and Planck's constant, and impulse and momentum are all pairs of physical quantities that have identical dimensions.
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Out of the following pairs one which does not have identical dimensions isa)Moment of inertia and moment of a forceb)Work and torquec)Angular momentum and planck's constantd)Impulse and momentumCorrect answer is option 'A'. Can you explain this answer?
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