Standards of Length, Mass, and Time

In summary, two spheres, one with a radius of 4.30 cm and the other with a mass two times greater, are cut from a uniform rock. Using the relation between the radius of a sphere and its volume, the radius of the second sphere can be found by setting the two relations of mass and volume equal to each other and solving for r2. The calculated radius is 5.4 cm.
  • #1
knightassassin
13
0
Two spheres are cut from a certain uniform rock. One has radius 4.30 cm. The mass of the other is two times greater. Find its radius.


Not sure what equations to use for it

I am not sure how to attempt this problem?
 
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  • #2
Mass is volume times density. 'Uniform' rock means you can assume the two rocks have the same uniform density. Now do you know a relation between the radius of a sphere and the volume?
 
  • #3
Volume equals (4/3)pi radius^3
 
  • #4
Good then you are all set to go. Try solving it.
 
  • #5
Thanks I got it. So I set the two relations equal to each other m1/v1=m2/v2. Substitute volume for their equation of (4/3)pi radius^3 and solve for r2.
 
  • #6
The answer I got was 5.4 cm, which is right thanks again.
 

FAQ: Standards of Length, Mass, and Time

What are the three fundamental units of measurement for length, mass, and time?

The three fundamental units of measurement for length, mass, and time are the meter, kilogram, and second, respectively. These are known as the International System of Units (SI) base units and are used as the basis for all other units of measurement.

How are standards of measurement determined and maintained?

Standards of measurement are determined and maintained by national and international organizations such as the National Institute of Standards and Technology (NIST) in the United States and the International Bureau of Weights and Measures (BIPM) globally. These organizations establish and maintain physical standards that represent the defined units of measurement.

What is the purpose of having standardized units of measurement?

The purpose of having standardized units of measurement is to provide a consistent and universal system for measuring quantities in order to facilitate accurate and reliable communication and comparison of data. It also allows for efficient scientific research and development, as well as international trade and commerce.

How have standards of measurement evolved over time?

Standards of measurement have evolved over time through the refinement and improvement of measurement techniques and technologies. For example, the meter was originally defined as one ten-millionth of the distance from the North Pole to the equator, but is now defined as the distance light travels in a vacuum in 1/299,792,458 of a second.

Are there any proposed changes to the current standards of measurement?

Yes, there are ongoing discussions and proposals for changes to the current standards of measurement, particularly in the areas of mass and time. For example, there have been discussions about redefining the kilogram to be based on a fundamental constant of nature instead of a physical object, and redefining the second to be based on the natural frequency of a cesium atom rather than the Earth's rotation.

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