Can dimensional analysis determine whether the area of a circle is πr2 or 2πr2? Explain.
Answer to Problem 1CQ
Explanation of Solution
Write the dimensional formula for the area of the circle
Here,
Write the dimensional formula for the area of the circle
Here,
From the equation (1) and (2) the dimension of the area is same in both cases. So that the dimensional analysis cannot be determine whether the area of a circle is
The dimensions of the variable do not depend on the numeric number.
Conclusion:
Therefore, the dimensional analysis cannot determine whether the area of a circle is
Want to see more full solutions like this?
Chapter 1 Solutions
Physics (5th Edition)
Additional Science Textbook Solutions
Essential University Physics: Volume 1 (3rd Edition)
Conceptual Integrated Science
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
University Physics with Modern Physics (14th Edition)
The Cosmic Perspective (8th Edition)
Essential University Physics (3rd Edition)
- A surveyor measures the distance across a straight river by the following method (Fig. P3.7). Starting directly across from a tree on the opposite bank, she walks d = 100 m along the riverbank to establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is = 35.0. How wide is the river?arrow_forwardFor the triangle shown in Figure P1.45, what are (a) the length of the unknown side, (b) the tangent of , and (c) the sine of ? Figure P1.45arrow_forwardA surveyor measures the distance across a straight river by the following method: starting directly across from a tree on the opposite bank, he walks x = 1.00 102 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline lo the tree is = 35.0 (Fig. P1.53). How wide is the river? Figure P1.53arrow_forward
- Answer each question yes or no. Must two quantities have the same dimensions (a) if you are adding them? (b) If you are multiplying them? (c) If you are subtracting them? (d) If you are dividing them? (e) If you are equating them?arrow_forwardA surveyor measures the distance across a straight river by the following method (Fig. P1.6). Starting directly across from a tree on the opposite bank, she walks d = 100 m along the riverbank to establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is 0 = 35.0. How wide is the river? Figure P1.6arrow_forwardA sidewalk is to be constructed around a swimming pool that measures (10.0 0.1) m by (17.0 0.1) m. If the sidewalk is to measure (1.00 0.01) m wide by (9.0 0.1) cm thick, what volume of concrete is needed and what is the approximate uncertainty of this volume?arrow_forward
- The Hoover Dam Bridge connecting Arizona and Nevada opened in October 2010 ( Fig. 1.18). It is the highest and longest arched concrete bridge in the Western Hemisphere, rising 890 ft above the Colorado River and extending 1900 ft in length. What are these dimensions in meters? Figure 1.18 High and Wide An aerial view of the new four-lane Hoover Dam Bridge between Arizona and Nevada with the Colorado River beneath (as seen from behind the dam). See Exercise 16.arrow_forwardA surveyor measures the distance across a straight river by the following method: starting directly across from a tree on the opposite bank, he walks x = 1.00 102 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline lo the tree is = 35.0 (Fig. P1.53). How wide is the river? Figure P1.53arrow_forwardAnswer each question yes or no. Must two quantities have the same dimensions (a) if you are adding them? (b) If you are multiplying them? (c) If you are subtracting them? (d) If you are dividing them? (e) If you are equating them?arrow_forward
- The purpose of this problem is to show the entire concept of dimensional consistency can be summarized but the old saying “You can’t add apples and oranges.” It you have studied power series expansions in a calculus course, you know the standard mathematical funstions such as trigonometric functions, logarithms, and exponential function can be expressed as infinite sums of the form where the an are dimensionless constants for all n = 0, 1, 2, … and x is the argument of the function. (If you have not studied power series in calculus yet, just trust us.) Use this fact to explain why the requirement that all terms in an equation have the same dimensions is sufficient as a definition of dimensional consistency. That is, it actually implies the arguments of standard mathematical funstions must be dimensional consistency. That is, it actually implies the arguments of standard mathematical functions must be dimensionless, so it is not really necessary to make this latter condition a separate requirement of the definition of dimensional consistency as we have done in this section.arrow_forwardHow many significant figures does each number have? If the number is exact or if the number of significant figures is ambiguous, explain. a. 12 in the formula r12d, where r is radius and d is diameter b. 105 c. 150 d. 1.50 102 e. 1.5 102 f. 0.15 103arrow_forwardIn general, when a derived unit becomes complicated (involves too many standard units), what is done?arrow_forward
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningAn Introduction to Physical SciencePhysicsISBN:9781305079137Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar TorresPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College