LT-2 is the dimension of which of the following quantities?
Understanding Dimensions in Physics
In physics, dimensions are the fundamental physical quantities that make up a measurement. The basic dimensions used are Mass (M), Length (L), and Time (T). Any physical quantity can be expressed in terms of combinations of these fundamental dimensions. This process is called dimensional analysis. The dimension of a quantity tells us about its physical nature, regardless of the units used to measure it (like meters, feet, seconds, minutes, kilograms, pounds).
The question asks for the quantity whose dimension is given as LT-2. Let's examine the dimensions of the quantities provided in the options.
Dimensional Analysis of Given Quantities
We will break down each quantity into its fundamental dimensions [M], [L], and [T].
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Power: Power is the rate at which work is done or energy is transferred.
- Work = Force × Distance
- Force = Mass × Acceleration
- Acceleration = Velocity / Time
- Velocity = Distance / Time
Starting from basic components:
- Dimension of Velocity: $[L][T]^{-1}$
- Dimension of Acceleration: $[Velocity] / [Time] = ([L][T]^{-1}) / [T] = [L][T]^{-2}$
- Dimension of Force: $[Mass] \times [Acceleration] = [M][L][T]^{-2}$
- Dimension of Work: $[Force] \times [Distance] = ([M][L][T]^{-2}) \times [L] = [M][L]^{2}[T]^{-2}$
- Dimension of Power: $[Work] / [Time] = ([M][L]^{2}[T]^{-2}) / [T] = [M][L]^{2}[T]^{-3}$
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Acceleration: Acceleration is the rate of change of velocity with respect to time.
- Acceleration = Velocity / Time
- Velocity = Distance / Time
Dimension of Velocity: $[L][T]^{-1}$
Dimension of Acceleration: $[Velocity] / [Time] = ([L][T]^{-1}) / [T] = [L][T]^{-2}$
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Momentum: Momentum is the product of mass and velocity.
- Momentum = Mass × Velocity
Dimension of Velocity: $[L][T]^{-1}$
Dimension of Momentum: $[Mass] \times [Velocity] = [M] \times ([L][T]^{-1}) = [M][L][T]^{-1}$
-
Density: Density is mass per unit volume.
- Density = Mass / Volume
- Volume = Length × Width × Height = Distance3
Dimension of Volume: $[L]^3$
Dimension of Density: $[Mass] / [Volume] = [M] / [L]^3 = [M][L]^{-3}$
Comparing Dimensions
Let's summarize the dimensions we found for each quantity in a table:
| Quantity | Dimension |
|---|---|
| Power | $[M][L]^{2}[T]^{-3}$ |
| Acceleration | $[L][T]^{-2}$ |
| Momentum | $[M][L][T]^{-1}$ |
| Density | $[M][L]^{-3}$ |
The question asks which quantity has the dimension LT-2. From our analysis and the table, the dimension of Acceleration is $[L][T]^{-2}$. This matches the given dimension LT-2.
Therefore, LT-2 is the dimension of Acceleration.
Important Questions from Dimensional formulae and dimensional equations
- Considering the Lorentz force $\vec{F} = q(\vec{v} \times \vec{B})$, where $F$ is force, $q$ is electric charge, and $v$ is velocity, what is the dimensional formula for magnetic flux density $B$?
- The characteristic impedance of free space, $Z_0$, is given by the expression $Z_0 = \sqrt{\frac{\mu_0}{\epsilon_0}}$. If $\mu_0$ represents the magnetic permeability and $\epsilon_0$ represents the electric permittivity, what are the dimensions of $Z_0$?
If \(x = a^3 + bt + ct^2\), where \(x\) is metres and \(t\) in seconds, then the unit of \(a\) is
- The dimensional formula of speed
The dimensions of energy are:
