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Which of the following pairs of physical quantities does not have same dimensional formula?
- a)Work and torque
- b)Angular momentum and Planck's constant
- c)Tension and surface tension
- d)Impulse and linear momentum.
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Which of the following pairs of physical quantities does not have same...
Explanation:
The dimensional formula is a way to express the physical quantity in terms of fundamental units. If two physical quantities have the same dimensional formula, it means they can be expressed in the same fundamental units.
Work and Torque:
- Work is defined as the product of force and displacement. Its dimensional formula is [ML²T⁻²].
- Torque is defined as the product of force and perpendicular distance from the axis of rotation. Its dimensional formula is [ML²T⁻²].
- Both work and torque have the same dimensional formula, [ML²T⁻²].
Angular Momentum and Planck's Constant:
- Angular momentum is defined as the product of moment of inertia and angular velocity. Its dimensional formula is [ML²T⁻¹].
- Planck's constant is a fundamental constant in quantum mechanics. Its dimensional formula is [ML²T⁻¹].
- Both angular momentum and Planck's constant have the same dimensional formula, [ML²T⁻¹].
Tension and Surface Tension:
- Tension is a force that is transmitted through a string, rope, or cable. Its dimensional formula is [MLT⁻²].
- Surface tension is a property of the surface of a liquid that allows it to resist an external force. Its dimensional formula is [MT⁻²].
- Tension and surface tension have different dimensional formulas, [MLT⁻²] and [MT⁻²] respectively.
Impulse and Linear Momentum:
- Impulse is the change in momentum of an object. Its dimensional formula is [MLT⁻¹].
- Linear momentum is the product of mass and velocity. Its dimensional formula is [MLT⁻¹].
- Both impulse and linear momentum have the same dimensional formula, [MLT⁻¹].
Therefore, the pair of physical quantities that does not have the same dimensional formula is Tension and Surface Tension (option C).
The dimensional formula is a way to express the physical quantity in terms of fundamental units. If two physical quantities have the same dimensional formula, it means they can be expressed in the same fundamental units.
Work and Torque:
- Work is defined as the product of force and displacement. Its dimensional formula is [ML²T⁻²].
- Torque is defined as the product of force and perpendicular distance from the axis of rotation. Its dimensional formula is [ML²T⁻²].
- Both work and torque have the same dimensional formula, [ML²T⁻²].
Angular Momentum and Planck's Constant:
- Angular momentum is defined as the product of moment of inertia and angular velocity. Its dimensional formula is [ML²T⁻¹].
- Planck's constant is a fundamental constant in quantum mechanics. Its dimensional formula is [ML²T⁻¹].
- Both angular momentum and Planck's constant have the same dimensional formula, [ML²T⁻¹].
Tension and Surface Tension:
- Tension is a force that is transmitted through a string, rope, or cable. Its dimensional formula is [MLT⁻²].
- Surface tension is a property of the surface of a liquid that allows it to resist an external force. Its dimensional formula is [MT⁻²].
- Tension and surface tension have different dimensional formulas, [MLT⁻²] and [MT⁻²] respectively.
Impulse and Linear Momentum:
- Impulse is the change in momentum of an object. Its dimensional formula is [MLT⁻¹].
- Linear momentum is the product of mass and velocity. Its dimensional formula is [MLT⁻¹].
- Both impulse and linear momentum have the same dimensional formula, [MLT⁻¹].
Therefore, the pair of physical quantities that does not have the same dimensional formula is Tension and Surface Tension (option C).
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Community Answer
Which of the following pairs of physical quantities does not have same...
Tension = [MLT−2]
Surface Tension = [ML0T−2]
Clearly these two have different dimension.
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Which of the following pairs of physical quantities does not have same dimensional formula?a)Work and torqueb)Angular momentum and Plancks constantc)Tension and surface tensiond)Impulse and linear momentum.Correct answer is option 'C'. Can you explain this answer?
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