Unit Conversion: G 6.67x10^-11 m^3*s^-2*kg^-1 to cm^3*s^2*g^-1

In summary, to convert from m^3*s^-2*kg^-1 to cm^3*s^2*g^-1, we can use the conversion factor of 1 m = 100 cm and 1 kg = 1000 g. The value of G in cm^3*s^2*g^-1 is 6.67x10^-8. G is expressed in units of m^3*s^-2*kg^-1 because it is a fundamental physical constant that relates the strength of the gravitational force between two objects to their masses and the distance between them. While G can be expressed in other unit systems, the most commonly used is the SI system. G is measured and determined through experiments involving the motion of celestial
  • #1
Hank_Rearden
25
0

Homework Statement


"The gravitational constant G is 6.67*10^-11 m^3*s^-2*kg^-1. What is G in units of cm^3*s^2*g^-1


Homework Equations


1kg = 1000g
1m = 100cm


The Attempt at a Solution



I don't understand how the dimension can change from [L^3,T^-2,M^-1] to [L^3,T^2,M^-1], shouldn't the dimension stay consistent even if the units change?
 
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  • #2
Yes, it's a typo, they are missing a minus sign on that "s" exponent.
 

1. How do I convert G from m^3*s^-2*kg^-1 to cm^3*s^2*g^-1?

To convert from m^3*s^-2*kg^-1 to cm^3*s^2*g^-1, we need to use the conversion factor of 1 m = 100 cm and 1 kg = 1000 g. This means that we can multiply the given value of G by (100 cm)^3/(1 m)^3 and (1000 g)/(1 kg) to get the equivalent value in cm^3*s^2*g^-1.

2. What is the value of G in cm^3*s^2*g^-1?

The value of G in cm^3*s^2*g^-1 is 6.67x10^-8.

3. Why is G expressed in units of m^3*s^-2*kg^-1?

G, also known as the gravitational constant, is a fundamental physical constant that relates the strength of the gravitational force between two objects to their masses and the distance between them. The units of m^3*s^-2*kg^-1 represent the proportionality constant in the equation for gravitational force, F = G*(m1*m2)/r^2, where m1 and m2 are the masses of the objects and r is the distance between them.

4. Can I use G in other unit systems, such as imperial or metric?

Yes, G can be expressed in different unit systems, but the most commonly used unit system for G is the SI (International System of Units) system, which uses meters, kilograms, and seconds as base units. However, it is important to note that the value of G may vary depending on the unit system used, so it is essential to use the correct unit conversion when working with this constant.

5. How is G measured and determined?

G is a very small and difficult constant to measure, as it requires very precise and sensitive equipment. It is typically determined through experiments involving the motion of celestial bodies, such as planets and stars. The most accurate and recent value of G was determined by the Cavendish experiment in 1798, which measured the gravitational force between two small lead spheres.

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