(III) The smallest meaningful measure of length is called the Planck length, and is defined in terms of three fundamental constants in nature: the speed of light c the gravitational constant G = 6.67 × 10-11 m³/kg•s², and Planck's constant h = 6.63 × 10-34 kg·m²/s. The Planck length {p is given by the following combination of these three constants: 3.00 × 10° m/s, Gh lp Show that the dimensions of lp are length [L], and find the order of magnitude of lp. [Recent theories (Chapters 32 and 33) suggest that the smallest particles (quarks, leptons) are “strings" with lengths on the order of the Planck length, 10-35 m. These theories also suggest that the “Big Bang," with which the universe is believed to have begun, started from an initial size on the order of the Planck length.]

(III) The smallest meaningful measure of length is called the Planck length, and is defined in terms of three fundamental constants in nature: the speed of light c the gravitational constant G = 6.67 × 10-11 m³/kg•s², and Planck's constant h = 6.63 × 10-34 kg·m²/s. The Planck length {p is given by the following combination of these three constants: 3.00 × 10° m/s, Gh lp Show that the dimensions of lp are length [L], and find the order of magnitude of lp. [Recent theories (Chapters 32 and 33) suggest that the smallest particles (quarks, leptons) are “strings" with lengths on the order of the Planck length, 10-35 m. These theories also suggest that the “Big Bang," with which the universe is believed to have begun, started from an initial size on the order of the Planck length.]

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Consider the physical quantities m, s, v, a, t, and r with dimensions [m] = M, [s] = L, [v] = LT–1, [a] = LT–2, [t] = T, and [r] = L. 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.
Question: The force F is given in terms of time t and distance x by F = [a sinct + b cosdx ] Then the dimensions of (atb)/(3cd) are given by A) [M][L][T1] B) [M][L²][T¯!] C) [M][L][T?] D) [M][L~!][T²] E) [M][L][T]
the radius of a sphere is measured to be [6.50+-0.20cm, and its mass is measured to be 1.85+-0.20kg . determin its density in kilogrammes per cubic metre and uncetainity in the density
The measurement of a physical quantity is 4.76 m with 1.47% uncertainty. Therefore, the measurement is likely to be between: * 4.63 m and 4.78 m. O 4.67 m and 4.80 m. 4.69 m and 4.83 m. 4.71 m and 4.85 m. 4.73 m and 4.88 m.
You measure how long it takes to boil 1 liter of water (starting at room temperature). You repeat the measurement 5 times and the measured times are (all in seconds) • 200 • 215 • 195 • 213 190 What is the uncertainty of your time measurement (don't worry about sig fig usage, answer to 1 decimal place)
calculate the following and express the answer in the proper number of significant figures: (3.245x0.035x9.0023)/(4.076x2.01x42.3)
A high tech company uses a satellite to measure the size of features on the surface of the earth. They use this technology to measure a particular rectangular field and find it's length to be 444 ± 1.8 in meters and it's width to be 198 ± 1.63 in meters. They plan to report the perimeter (sum of two lengths and two widths) of the field as P± SP in units of yards. (1 meter = 1.094 yards) What is SP?
You measure two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report correct value for √AB as: (a) 1.4 m ± 0.4 m (b) 1.41m ± 0.15 m (c) 1.4m ± 0.3 m (d) 1.4m ± 0.2 m
Given that the Diameter of Earth is about 7200 miles, how many Earths would fit across the Sun? You turn toward the east, seeing the full moon rising. You find that half of your finger tip at arm's length also covers the diameter of the Moon! Given that the diameter of the Moon is about 2160 miles, approximately how far from Earth is the Moon in miles and km according to your calculations?
If the polar coordinates of a point are (r, φ) and its rectangular coordinates are (x, y) , determine the polar coordinates of the following points: (a) (−x, y), (b) (−2x, −2y), and (c) (3x, −3y).