1. Intro to Physics Units

Which of the following equations is dimensionally consistent?

In the equation $\frac{Gmm}{x^2}$ = $\frac{m{v}^2}{x}$, where the two $m$'s represent different masses, what are the SI units on each side of the equation?

Which of the following pairs of physical quantities and their dimensions is mismatched?

The speed v of an object is given by the equation v = At³ ― Bt, where t refers to time. What are the SI units for the constants A and B?

A force of $15.0n$ is applied to an object. Using the conversions $1\mathrm{slug}=14.59\mathrm{kg}$ and $1\mathrm{ft}=0.3048m$, what is the value of this force in pounds ($\mathrm{lb}$)?

Which of the following equations is dimensionally consistent?

Which of the following terms is correctly matched to its description in the context of dimensional analysis?

Which of the following pairs of terms is mismatched in terms of their dimensional analysis?

Which of the following pairings of physical quantities and their dimensions is correct?

Which of the following patterns is consistent with the principle of dimensional analysis?

In the context of dimensional analysis and measurement, parallel alignment error (also known as parallax error) can occur in how many dimensions?

Dimensional analysis. Waves on the surface of the ocean do not depend significantly on the properties of water such as density or surface tension. The primary 'return force' for water piled up in the wave crests is due to the gravitational attraction of the Earth. Thus the speed v (m/s) of ocean waves depends on the acceleration due to gravity g. It is reasonable to expect that υ might also depend on water depth h and the wave's wavelength λ. Assume the wave speed is given by the functional form v = Cgᵅ hᵝ λᵞ, where α , β , c and C are numbers without dimension. In deep water, the water deep below the surface does not affect the motion of waves at the surface. Thus υ should be independent of depth h (i.e., β = 0). Using only dimensional analysis (Section 1–7 and Appendix D), determine the formula for the speed of surface ocean waves in deep water.

Are the units of the formula $ma=m{v}^2/2$ dimensionally consistent? Select the single best answer.

The position of a ball rolling in a straight line is given by 𝓍 = 2.0 ― 3.6t + 1.7t², where 𝓍 is in meters and t in seconds. What do the numbers 2.0, 3.6, and 1.7 refer to?

Which one of the following pairs is mismatched in terms of dimensional analysis?