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Among the following pairs, which one does not have identical dimensions?
- 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
Among the following pairs, which one does not have identical dimension...
Moment of inertia (I) = mr2
[I] = [ML2]
Moment of force (C) = rF
[C] = [r][F] = [L][MLT-2] or [C] = [ML2T-2]
Moment of inertia and moment of a force do not have identical dimensions.
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Among the following pairs, which one does not have identical dimension...
Explanation:
Moment of inertia and Moment of a force:
- Moment of inertia is a measure of an object's resistance to changes in its rotation.
- Moment of a force, on the other hand, refers to the rotational effect of a force about a specific point.
- These two quantities do not have identical dimensions. Moment of inertia is measured in kg m², while moment of a force is measured in Nm.
Work and Torque:
- Work is the product of force and displacement in the direction of the force, measuring the amount of energy transferred to an object.
- Torque, on the other hand, is the rotational equivalent of force, measuring the tendency of a force to rotate an object about an axis.
- Work is measured in joules (J), while torque is measured in newton-meters (Nm).
Angular momentum and Planck's constant:
- Angular momentum is a measure of an object's rotational motion, calculated as the product of its moment of inertia and angular velocity.
- Planck's constant, on the other hand, is a fundamental physical constant that relates the energy of a photon to its frequency.
- These two quantities do not have identical dimensions. Angular momentum is measured in kg m²/s, while Planck's constant is measured in J s.
Impulse and Momentum:
- Impulse is the change in momentum of an object when a force is applied for a certain amount of time.
- Momentum, on the other hand, is the product of an object's mass and velocity, measuring its motion.
- Impulse and momentum have identical dimensions, both measured in kg m/s.
Moment of inertia and Moment of a force:
- Moment of inertia is a measure of an object's resistance to changes in its rotation.
- Moment of a force, on the other hand, refers to the rotational effect of a force about a specific point.
- These two quantities do not have identical dimensions. Moment of inertia is measured in kg m², while moment of a force is measured in Nm.
Work and Torque:
- Work is the product of force and displacement in the direction of the force, measuring the amount of energy transferred to an object.
- Torque, on the other hand, is the rotational equivalent of force, measuring the tendency of a force to rotate an object about an axis.
- Work is measured in joules (J), while torque is measured in newton-meters (Nm).
Angular momentum and Planck's constant:
- Angular momentum is a measure of an object's rotational motion, calculated as the product of its moment of inertia and angular velocity.
- Planck's constant, on the other hand, is a fundamental physical constant that relates the energy of a photon to its frequency.
- These two quantities do not have identical dimensions. Angular momentum is measured in kg m²/s, while Planck's constant is measured in J s.
Impulse and Momentum:
- Impulse is the change in momentum of an object when a force is applied for a certain amount of time.
- Momentum, on the other hand, is the product of an object's mass and velocity, measuring its motion.
- Impulse and momentum have identical dimensions, both measured in kg m/s.
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Among the following pairs, which one does not have identical dimensions?a)Moment of inertia and Moment of a forceb)Work and Torquec)Angular momentum and Plancks constantd)Impulse and MomentumCorrect answer is option 'A'. Can you explain this answer?
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