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Questions and Answers
What is the dimensional formula for velocity?
What is the dimensional formula for velocity?
- [M^0 L^1 T^{-1}] (correct)
- [M^1 L^1 T^{-1}]
- [M^0 L^1 T^1]
- [M^1 L^0 T^1]
In the dimensional formula for velocity, what does the exponent of time represent?
In the dimensional formula for velocity, what does the exponent of time represent?
- It signifies the direct relationship with time.
- It denotes a squared relationship with time.
- It reflects an inverse relationship with time. (correct)
- It indicates the absence of time dimension.
Which of the following represents the dimensions of the fundamental quantity mass?
Which of the following represents the dimensions of the fundamental quantity mass?
- [M^0 L^0 T^1]
- [M^0 L^1 T^0]
- [M^1 L^1 T^0]
- [M^1 L^0 T^0] (correct)
What is indicated by the dimensional formula [M^0 L^1 T^{-1}]?
What is indicated by the dimensional formula [M^0 L^1 T^{-1}]?
What type of quantity does the dimension [L^1 T^{-1}] specifically imply?
What type of quantity does the dimension [L^1 T^{-1}] specifically imply?
What does the slope of a displacement-time graph represent?
What does the slope of a displacement-time graph represent?
At which point does the particle have zero velocity?
At which point does the particle have zero velocity?
If the displacement-time graph shows a downward slope, what can be inferred about the particle's velocity?
If the displacement-time graph shows a downward slope, what can be inferred about the particle's velocity?
What happens to the velocity of the particle at time t1 according to the displacement-time graph?
What happens to the velocity of the particle at time t1 according to the displacement-time graph?
What does the graph indicate about the velocity of the particle at time t3?
What does the graph indicate about the velocity of the particle at time t3?
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Study Notes
Dimensions of Physical Quantities
- The dimensions of a physical quantity are the powers to which the fundamental quantities must be raised.
- The fundamental quantities are mass (M), length (L), and time (T).
- The dimensional formula for a quantity represents its dimensions in terms of the fundamental quantities.
Example: Velocity
- Velocity is the displacement over time.
- Velocity's dimensional formula is [M⁰L¹T⁻¹] or simply [LT⁻¹].
- [M⁰L¹T⁻¹] indicates that velocity has zero dimensions in mass, one dimension in length, and -1 dimension in time.
Dimensional Formula for Other Quantities
- The dimensions of fundamental quantities are given in a table.
- The dimensions of some derived quantities are given in a table.
Displacement-Time Graph
- A displacement-time graph shows the position of a particle over time.
- The slope of the displacement-time graph at any point gives the velocity of the particle at that instant.
- A positive slope indicates a positive velocity.
- A zero slope indicates zero velocity.
- A negative slope indicates a negative velocity.
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