1. earth
2. solar system
3. milky way galaxy
4. local group of galaxies
5. universe
Answer:
a
The orbital speed is ![v= 2.6*10^{3} m/s](https://tex.z-dn.net/?f=v%3D%202.6%2A10%5E%7B3%7D%20m%2Fs)
b
The escape velocity of the rocket is ![v_e= 3.72 *10^3 m/s](https://tex.z-dn.net/?f=v_e%3D%203.72%20%2A10%5E3%20m%2Fs)
Explanation:
Generally angular velocity is mathematically represented as
Where T is the period which is given as 1.6 days = ![1.6 *24 *60*60 = 138240 sec](https://tex.z-dn.net/?f=1.6%20%2A24%20%2A60%2A60%20%3D%20138240%20sec)
Substituting the value
![w = \frac{2 \pi}{138240}](https://tex.z-dn.net/?f=w%20%3D%20%5Cfrac%7B2%20%5Cpi%7D%7B138240%7D)
![= 4.54*10^ {-5} rad /sec](https://tex.z-dn.net/?f=%3D%204.54%2A10%5E%20%7B-5%7D%20rad%20%2Fsec)
At the point when the rocket is on a circular orbit
The gravitational force = centripetal force and this can be mathematically represented as
![\frac{GMm}{r^2} = mr w^2](https://tex.z-dn.net/?f=%5Cfrac%7BGMm%7D%7Br%5E2%7D%20%3D%20mr%20w%5E2)
Where G is the universal gravitational constant with a value ![G = 6.67*10^{-11}](https://tex.z-dn.net/?f=G%20%3D%206.67%2A10%5E%7B-11%7D)
M is the mass of the earth with a constant value of ![M = 5.98*10^{24}kg](https://tex.z-dn.net/?f=M%20%3D%205.98%2A10%5E%7B24%7Dkg)
r is the distance between earth and circular orbit where the rocke is found
Making r the subject
![r = \sqrt[3]{\frac{GM}{w^2} }](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7BGM%7D%7Bw%5E2%7D%20%7D)
![= \sqrt[3]{\frac{6.67*10^{-11} * 5.98*10^{24}}{(4.45*10^{-5})^2} }](https://tex.z-dn.net/?f=%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B6.67%2A10%5E%7B-11%7D%20%2A%205.98%2A10%5E%7B24%7D%7D%7B%284.45%2A10%5E%7B-5%7D%29%5E2%7D%20%7D)
![= 5.78 *10^7 m](https://tex.z-dn.net/?f=%3D%205.78%20%2A10%5E7%20m)
The orbital speed is represented mathematically as
![v=wr](https://tex.z-dn.net/?f=v%3Dwr)
Substituting value
![v= (5.78*10^7)(4.54*10^{-5})](https://tex.z-dn.net/?f=v%3D%20%285.78%2A10%5E7%29%284.54%2A10%5E%7B-5%7D%29)
The escape velocity is mathematically represented as
![v_e = \sqrt{\frac{2GM}{r} }](https://tex.z-dn.net/?f=v_e%20%3D%20%5Csqrt%7B%5Cfrac%7B2GM%7D%7Br%7D%20%7D)
Substituting values
![= \sqrt{\frac{2(6.67*10^{-11})(5.98*10^{24})}{5.78*10^7} }](https://tex.z-dn.net/?f=%3D%20%5Csqrt%7B%5Cfrac%7B2%286.67%2A10%5E%7B-11%7D%29%285.98%2A10%5E%7B24%7D%29%7D%7B5.78%2A10%5E7%7D%20%7D)
![v_e= 3.72 *10^3 m/s](https://tex.z-dn.net/?f=v_e%3D%203.72%20%2A10%5E3%20m%2Fs)
Answer:
a) 4
b) 2
c) 8
Explanation:
In a cubic lattice, each atom of the vertex is shared among other 8 unit cells, so the atoms on the vertex contribute to 1/8 to a given unit cell.
a) Ina face-centered cubic we have 8 atoms on the vertex and one in each face, which is shared with another unit cell, so it contribute to 1/2
Therefore, the total atoms are:
8*(1/8) + 6*(1/2) = 4
b) In the body centered cubic structure, the centered atom is not shared with another cell, therefore it contribute to 1 to the given cell:
The number of atoms per unit cel is:
8*(1/8) + 1 = 2
c) The diamond lattice is similar to the face-centered cubic lattice but it contains two identical atoms per lattice point.
Therefore it must contain twice atoms than the face-centered cubic lattice:
that is, it has 8 atoms per unit cell
capacitance of any given capacitor is given by the formula,
C=Q/V
where C=capacitance,Q= charge and V=voltage
therefore from the formula capacitance is charge per unit voltage.