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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?
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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