Which of the following statements is correct? OAf an equation.is dimensionally correct it must be true and if it is not dimensionally correct it may be true. On Jf an equation is dimensionally çorrect it.muşt be true and if an equation is not dinmensionally correct it cannot be true. ocf an equątion is dimensionally, correct it may be cannot bê true. Oo If an equątion is dimensionally.correct it may be true and if an equation is not dimensionally correct it may bé true.

Which of the following statements is correct? OAf an equation.is dimensionally correct it must be true and if it is not dimensionally correct it may be true. On Jf an equation is dimensionally çorrect it.muşt be true and if an equation is not dinmensionally correct it cannot be true. ocf an equątion is dimensionally, correct it may be cannot bê true. Oo If an equątion is dimensionally.correct it may be true and if an equation is not dimensionally correct it may bé true.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter1: Units And Measurement

Section: Chapter Questions

Problem 52P: Consider the physical quantities m,s,v,a, and t with dimensions [m]=M,[s]=L,[v]=LT1 and [a]=LT2 ....

See similar textbooks

Similar questions

A block of gold has length 5.62 cm. width 6.35 cm, and height 2.78 cm. (a) Calculate the length times the width and round the answer to the appropriate number of significant figures. (b) Now multiply the rounded result of part (a) by the height and again round, obtaining the volume. (c) Repeat the process, first finding the width limes the height, founding it, and then obtaining the volume by multiplying by the length. (d) Explain why the answers dont agree in the third significant figure.
Consider the equation y=mt+b, where the dimension of y is length and the dimension of t is time, and mand bare constants. What are the dimensions and SI units of (a) mand (b) b ?
Consider the physical quantities m,s,v,a, and t with dimensions [m]=M,[s]=L,[v]=LT1 and [a]=LT2 . Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation: (a)F=ma;(b)K=0.5mv2;(c)p=mv;(d)W=mas;(e)L=mvr
A student is trying to remember some formulas from geometry. In what follows, assume Ais area, Vis volume, and all other variables are lengths. Determine which formulas are dimensionally consistent. (a) V=r2h; (b) A=2r2+2rh; (c) V=0.5bh(d) V=d2; (e) V=d3/6.
A rectangular airstrip measures 32.30 m by 210 m, with the width measured more accurately than the length. Find the area, taking into account significant figures. (See Section 1.4.)
In general, when a derived unit becomes complicated (involves too many standard units), what is done?
Check Your understanding Using the three displacement vectors A , B , and F in Figure 2.13, choose a convenient scale, and use a ruler and a protractor to find vector G given by the vector equation G=A+2BF . The three displacement vectors A , B , and C in Figure are specified by their magnitudes A=10.0,B=7.0 and C=8.0 , respectively, and by their respective direction angles with the horizontal direction =35,=110 , and =30 . The physical units of the magnitudes are centimeters. Choose a convenient scale and use a ruler and a protractor to find the following vector sums: (a) R=A+B , (b) D=AB , and (c) S=A3B+C .
Consider the equation 4000/400=10.0 . Assuming the number of significant figures in the answer is correct, what can you say about the number of significant figures In 4000 and 400?
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.
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?
How 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. 0.15 103
Check Your Understanding Restate 4.79105kg using a metric prefix such that the resulting number is bigger than one but less than 1000.