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Dimensions of Physical Quantities Quiz

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Questions and Answers

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?

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?

[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}]?

It represents velocity. Signup and view all the answers

What type of quantity does the dimension [L^1 T^{-1}] specifically imply?

Velocity Signup and view all the answers

What does the slope of a displacement-time graph represent?

The velocity of the particle Signup and view all the answers

At which point does the particle have zero velocity?

At time t2 Signup and view all the answers

If the displacement-time graph shows a downward slope, what can be inferred about the particle's velocity?

The particle has negative velocity Signup and view all the answers

What happens to the velocity of the particle at time t1 according to the displacement-time graph?

It becomes positive Signup and view all the answers

What does the graph indicate about the velocity of the particle at time t3?

The velocity is negative Signup and view all the answers

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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Description

Test your understanding of the dimensions of physical quantities, including fundamental quantities like mass, length, and time. This quiz covers concepts such as dimensional formulas and examples like velocity. Dive into the world of dimensional analysis and solidify your grasp on the topic.