Show the demension of the following. i) speed ii) density iii) force

General
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Show the demension of the following. i) speed ii) density iii) force.

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What are the dimension formulas for speed, density, and force?

To provide the dimension formulas for speed, density, and force, we can break down each of these physical quantities into their basic dimensions. In physics, dimensions are represented using the base quantities: Mass (M), Length (L), Time (T), Current (I), Temperature (\Theta), Amount of substance (N), and Luminous intensity (J). Let’s work through each of these quantities one by one.

i) Speed

Speed is defined as the rate at which an object covers distance. It is calculated by dividing the distance traveled by the time taken. Therefore, the formula for speed is:

\text{Speed} = \frac{\text{Distance}}{\text{Time}}

Dimension Formula for Speed:

Given that the dimension of length is [L] and that of time is [T], the dimension formula for speed can be expressed as:

  • Length = L
  • Time = T
\text{Dimension of Speed} = \frac{[L]}{[T]} = [L T^{-1}]

Thus, the dimension of speed is [L T^{-1}].

ii) Density

Density is defined as the mass per unit volume of a substance. It describes how much mass is contained in a given volume. The formula for density is:

\text{Density} = \frac{\text{Mass}}{\text{Volume}}

Dimension Formula for Density:

For density, note that mass is represented as [M] and volume (being a cubic measure of length) is [L^3]. The dimension formula for density is:

  • Mass = M
  • Volume = [L^3]
\text{Dimension of Density} = \frac{[M]}{[L^3]} = [M L^{-3}]

Thus, the dimension of density is [M L^{-3}].

iii) Force

Force is defined as any interaction that, when unopposed, will change the motion of an object. According to Newton’s Second Law of Motion, force is the product of mass and acceleration. The formula for force is:

\text{Force} = \text{Mass} \times \text{Acceleration}

Dimension Formula for Force:

Acceleration itself is the change in velocity over time, which can be dimensionally represented as:

  • Velocity = [L T^{-1}], so
  • Acceleration = [L T^{-2}] (because it’s velocity change per time unit)

Given that mass is [M], the dimension for force becomes:

\text{Dimension of Force} = [M] \times [L T^{-2}] = [M L T^{-2}]

Thus, the dimension of force is [M L T^{-2}].

By breaking these quantities into basic dimensions, we’ve given concrete dimensional interpretations that aid in understanding their relationships and dependencies in physical equations. If you have any further questions about dimensions or related topics, feel free to ask! @anonymous10