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Out of the following pairs, choose the pair in which the physical quantities do not have identical dimension?
- a)Pressure and Young's modules
- b)Planck's constant and Angular momentum
- c)Impulse and moment of force
- d)Force and rate of change of linear momentum
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Out of the following pairs, choose the pair in which the physical quan...
Understanding Physical Quantities
In physics, it is crucial to compare the dimensions of different physical quantities to understand their relationships. Let's analyze the pairs mentioned in the question.
Pair Analysis
- Pressure and Young's Modulus
- Both quantities have dimensions of force per unit area (ML^-1T^-2). Therefore, they have identical dimensions.
- Planck's Constant and Angular Momentum
- Planck's constant (h) has dimensions of energy multiplied by time (ML^2T^-1), while angular momentum (L) also has dimensions of (ML^2T^-1). They share identical dimensions.
- Impulse and Moment of Force
- Impulse is defined as the change in momentum, with dimensions of (MLT^-1). Moment of force (torque) has dimensions of (ML^2T^-2). Thus, their dimensions differ, making this pair unique.
- Force and Rate of Change of Linear Momentum
- Force is defined as (MLT^-2) and the rate of change of linear momentum also has dimensions of (MLT^-2). Therefore, they have identical dimensions.
Conclusion
The correct answer is option 'C' because impulse and moment of force are the only pair that does not share identical dimensions. Understanding these distinctions is essential for grasping the fundamental principles of physics.
In physics, it is crucial to compare the dimensions of different physical quantities to understand their relationships. Let's analyze the pairs mentioned in the question.
Pair Analysis
- Pressure and Young's Modulus
- Both quantities have dimensions of force per unit area (ML^-1T^-2). Therefore, they have identical dimensions.
- Planck's Constant and Angular Momentum
- Planck's constant (h) has dimensions of energy multiplied by time (ML^2T^-1), while angular momentum (L) also has dimensions of (ML^2T^-1). They share identical dimensions.
- Impulse and Moment of Force
- Impulse is defined as the change in momentum, with dimensions of (MLT^-1). Moment of force (torque) has dimensions of (ML^2T^-2). Thus, their dimensions differ, making this pair unique.
- Force and Rate of Change of Linear Momentum
- Force is defined as (MLT^-2) and the rate of change of linear momentum also has dimensions of (MLT^-2). Therefore, they have identical dimensions.
Conclusion
The correct answer is option 'C' because impulse and moment of force are the only pair that does not share identical dimensions. Understanding these distinctions is essential for grasping the fundamental principles of physics.
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Community Answer
Out of the following pairs, choose the pair in which the physical quan...
To determine which pair of physical quantities does not have identical dimensions, we need to compare their units.
Let's analyze each pair:
A: Pressure and Young's modulus
- Pressure is measured in units of force divided by area, such as pascals (Pa) or N/m^2.
- Young's modulus is measured in units of force divided by area, such as pascals (Pa) or N/m^2.
- Both pressure and Young's modulus have the same dimensions and units, so they have identical dimensions.
B: Planck's constant and Angular momentum
- Planck's constant is measured in units of energy multiplied by time, such as joule-seconds (J·s).
- Angular momentum is measured in units of mass multiplied by length squared divided by time, such as kg·m^2/s.
- Planck's constant and angular momentum have different dimensions and units, so they do not have identical dimensions.
C: Impulse and moment of force
- Impulse is measured in units of force multiplied by time, such as newton-seconds (N·s).
- Moment of force (also known as torque) is measured in units of force multiplied by length, such as newton-meters (N·m).
- Impulse and moment of force have different dimensions and units, so they do not have identical dimensions.
D: Force and rate of change of linear momentum
- Force is measured in units of mass multiplied by length divided by time squared, such as newtons (N).
- Rate of change of linear momentum is measured in units of mass multiplied by length divided by time squared, such as newtons (N).
- Both force and rate of change of linear momentum have the same dimensions and units, so they have identical dimensions.
Therefore, the pair in which the physical quantities do not have identical dimensions is C: Impulse and moment of force.
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Out of the following pairs, choose the pair in which the physical quantities do not have identical dimension?a)Pressure and Young's modulesb)Planck's constant and Angular momentumc)Impulse and moment of forced)Force and rate of change of linear momentumCorrect answer is option 'C'. Can you explain this answer?
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