Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 1, Problem 38P
To determine

To write: The dimension and SI unit of the constant G .

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Newton’s law of universal gravitation is represented byF = G Mm r 2where F is the gravitational force, M and m are masses, and r is a length. Force has the SI units kg · m/s 2 . What are the SI units of the proportionality constant G?
Schwarzschild radius RS of a black hole is the maximum distance from the black hole’s center at which light cannot escape its gravitational field. The quantity RS (with dimensions of length) is dependent on the mass of the black hole M, the speed of light c, and the gravitational constant G. Based on the dimensions of these four parameters, predict an equation for the Schwarzschild radius. Hint: G has dimensions of [L3/MT2]
In astronomy, a unit of distance is used called the Astronomical Unit. It is the average distance from the Earth to the Sun. If 1 au is 1.49 × 1011 m, and a light-year is the distance it takes light to travel in 1 year elapsed time (light travels at a speed of c = 3.0 x 108 ), then how many au is it to get to Alpha Centauri (our closest star with a planetary system) if is 4.367 lightyears away?
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