Here is the full question
Suppose there are 10,000 civilizations in the Milky Way Galaxy. If the civilizations were randomly distributed throughout the disk of the galaxy, about how far (on average) would it be to the nearest civilization?
(Hint: Start by finding the area of the Milky Way's disk, assuming that it is circular and 100,000 light-years in diameter. Then find the average area per civilization, and use the distance across this area to estimate the distance between civilizations.)
Answer:
1000 light-years (ly)
Explanation:
If we go by the hint; The area of the disk can be expressed as:
![A = \pi (\frac{D}{2})^2](https://tex.z-dn.net/?f=A%20%3D%20%5Cpi%20%28%5Cfrac%7BD%7D%7B2%7D%29%5E2)
where D = 100, 000 ly
Let's divide the Area by the number of civilization; if we do that ; we will be able to get 'n' disk that is randomly distributed; so ;
![d= \frac{A}{N} =\frac{\pi (\frac{D}{2})^2 }{10, 000}](https://tex.z-dn.net/?f=d%3D%20%5Cfrac%7BA%7D%7BN%7D%20%3D%5Cfrac%7B%5Cpi%20%28%5Cfrac%7BD%7D%7B2%7D%29%5E2%20%7D%7B10%2C%20000%7D)
The distance between each disk is further calculated by finding the radius of the density which is shown as follows:
![d = \pi r^2 e](https://tex.z-dn.net/?f=d%20%3D%20%5Cpi%20r%5E2%20e)
![r^2_e= \frac{d}{\pi}](https://tex.z-dn.net/?f=r%5E2_e%3D%20%5Cfrac%7Bd%7D%7B%5Cpi%7D)
![r_e = \sqrt{\frac{d}{\pi} }](https://tex.z-dn.net/?f=r_e%20%3D%20%5Csqrt%7B%5Cfrac%7Bd%7D%7B%5Cpi%7D%20%7D)
replacing d =
in the equation above; we have:
![r_e = \sqrt{\frac{\frac{\pi (\frac{D}{2})^2 }{10, 000}}{\pi} }](https://tex.z-dn.net/?f=r_e%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Cfrac%7B%5Cpi%20%28%5Cfrac%7BD%7D%7B2%7D%29%5E2%20%7D%7B10%2C%20000%7D%7D%7B%5Cpi%7D%20%7D)
![r_e = \sqrt{\frac{(\frac{D}{2})^2 }{10, 000}}](https://tex.z-dn.net/?f=r_e%20%3D%20%5Csqrt%7B%5Cfrac%7B%28%5Cfrac%7BD%7D%7B2%7D%29%5E2%20%7D%7B10%2C%20000%7D%7D)
![r_e = \sqrt{\frac{(\frac{100,000}{2})^2 }{10, 000}}](https://tex.z-dn.net/?f=r_e%20%3D%20%5Csqrt%7B%5Cfrac%7B%28%5Cfrac%7B100%2C000%7D%7B2%7D%29%5E2%20%7D%7B10%2C%20000%7D%7D)
![r_e = 500 ly](https://tex.z-dn.net/?f=r_e%20%3D%20500%20ly)
The distance (s) between each civilization = ![2(r_e)](https://tex.z-dn.net/?f=2%28r_e%29)
= 2 (500 ly)
= 1000 light-years (ly)
Answer:
b is the correct option.
Explanation:
Steam distillation is a distillation in which water is added to the mixture being distilled so that water and the organic compounds vaporize, condense and are collected together. This process is applied for the purification of those materials specially the organic materials which are temperature sensitive. The normal boiling method can not be implemented as these materials starts to decompose on high temperatures. This method has got a lot of applications in industries like petrolium refineries and the oil extraction from some plants etc.
1) the weight of an object at Earth's surface is given by
![F=mg](https://tex.z-dn.net/?f=F%3Dmg)
, where m is the mass of the object and
![g=9.81 m/s^2](https://tex.z-dn.net/?f=g%3D9.81%20m%2Fs%5E2)
is the gravitational acceleration at Earth's surface. The book in this problem has a mass of m=2.2 kg, therefore its weight is
![F=mg=(2.2 kg)(9.81 m/s^2)=21.6 N](https://tex.z-dn.net/?f=F%3Dmg%3D%282.2%20kg%29%289.81%20m%2Fs%5E2%29%3D21.6%20N)
2) On Mars, the value of the gravitational acceleration is different:
![g=3.7 m/s^2](https://tex.z-dn.net/?f=%20g%3D3.7%20m%2Fs%5E2)
. The formula to calculate the weight of the object on Mars is still the same, but we have to use this value of g instead of the one on Earth:
![F=mg=(2.2 kg)(3.7 m/s^2)=8.1 N](https://tex.z-dn.net/?f=F%3Dmg%3D%282.2%20kg%29%283.7%20m%2Fs%5E2%29%3D8.1%20N)
3) The weight of the textbook on Venus is F=19.6 N. We already know its mass (m=2.2 kg), therefore by re-arranging the usual equation F=mg, we can find the value of the gravitational acceleration g on Venus:
![g= \frac{F}{m}= \frac{ 19.6 N}{2.2 kg}=8.9 m/s^2](https://tex.z-dn.net/?f=g%3D%20%5Cfrac%7BF%7D%7Bm%7D%3D%20%5Cfrac%7B%2019.6%20N%7D%7B2.2%20kg%7D%3D8.9%20m%2Fs%5E2)
4) The mass of the pair of running shoes is m=0.5 kg. Their weight is F=11.55 N, therefore we can find the value of the gravitational acceleration g on Jupiter by re-arranging the usual equation F=mg:
![g= \frac{F}{m} = \frac{11.55 N}{0.5 kg} =23.1 m/s^2](https://tex.z-dn.net/?f=g%3D%20%5Cfrac%7BF%7D%7Bm%7D%20%3D%20%5Cfrac%7B11.55%20N%7D%7B0.5%20kg%7D%20%3D23.1%20m%2Fs%5E2)
5) The weight of the pair of shoes of m=0.5 kg on Pluto is F=0.3 N. As in the previous step, we can calculate the strength of the gravity g on Pluto as
![g= \frac{F}{m} = \frac{0.3 N}{0.5 kg} =0.6 m/s^2](https://tex.z-dn.net/?f=g%3D%20%5Cfrac%7BF%7D%7Bm%7D%20%3D%20%5Cfrac%7B0.3%20N%7D%7B0.5%20kg%7D%20%3D0.6%20m%2Fs%5E2)
<span>6) On Earth, the gravity acceleration is </span>
![g=9.81 m/s^2](https://tex.z-dn.net/?f=g%3D9.81%20m%2Fs%5E2)
<span>. The mass of the pair of shoes is m=0.5 kg, therefore their weight on Earth is
</span>
![F=mg=(0.5 kg)(9.81 m/s^2)=4.9 N](https://tex.z-dn.net/?f=F%3Dmg%3D%280.5%20kg%29%289.81%20m%2Fs%5E2%29%3D4.9%20N)
<span>
</span>