Answer:
6.18 um
Explanation:
The plumb line will be pulled down by a combination of the gravitationall pull of Earth and of the mountain. The Earth pulls down and the mountain to the side. Because of this it will fall not in a straight line down, but slightly to the side. Since the plumb line will follow the compound gravity we can imagine a rectangle triangle formed by the plumb line, a vertical line that ends at the same height as the plumb line, and the sideways displacement.
The total gravity will be proportional to the plumb line lenght, the vertical line will be proportional to Earth's gravity and the sideways displacement to the mountain pull.
The gravity of Earth is 9.81 m/s^2
The pull of the mountain will be defined by Newton's law of universal gravitation:
![F = G \frac{m1 * m2}{r^2}](https://tex.z-dn.net/?f=F%20%3D%20G%20%5Cfrac%7Bm1%20%2A%20m2%7D%7Br%5E2%7D)
Where
F: pull force
G: universal gravitational constant (6.67e-11 m^3/(kg * s)
m1: mass of the mountain
m2: mass of the plumb
r: distance between mountain and plumb (3 km in this case)
If we divide both sides by m2 we obtain the acceleration towards the mountain of the plumb
![a = G \frac{m1}{r^2}](https://tex.z-dn.net/?f=a%20%3D%20G%20%5Cfrac%7Bm1%7D%7Br%5E2%7D)
Now we need the mass of the mountain. This will be its volume times it's density. The volume depends on the radius (since we consider it as a sphere)
![m1 = \delta * \frac{4}{3} * \pi * r^3](https://tex.z-dn.net/?f=m1%20%3D%20%5Cdelta%20%2A%20%5Cfrac%7B4%7D%7B3%7D%20%2A%20%5Cpi%20%2A%20r%5E3)
![m1 = 2.6e3 * \frac{4}{3} * \pi * 1000^3 = 1.09e13 kg](https://tex.z-dn.net/?f=m1%20%3D%202.6e3%20%2A%20%5Cfrac%7B4%7D%7B3%7D%20%2A%20%5Cpi%20%2A%201000%5E3%20%3D%201.09e13%20kg)
So, the acceleration on the plumb will be
![a = 6.67e-11 \frac{1.09e13}{3000^2} = 8.08e-5 m/s^2](https://tex.z-dn.net/?f=a%20%3D%206.67e-11%20%5Cfrac%7B1.09e13%7D%7B3000%5E2%7D%20%3D%208.08e-5%20m%2Fs%5E2)
This is very small compared to the pull of Earth, so we can make an approximation that the length of the plumb line is equal to vertical line.
We can use the principle of similar triangles to say that:
![\frac{\Delta x}{L} = \frac{a}{g}](https://tex.z-dn.net/?f=%5Cfrac%7B%5CDelta%20x%7D%7BL%7D%20%3D%20%5Cfrac%7Ba%7D%7Bg%7D)
So:
![\Delta x = \frac{a * L}{g} = \frac{8.08e-5 * 0.75}{9.81} = 6.18e-6 m = 6.18 um](https://tex.z-dn.net/?f=%5CDelta%20x%20%3D%20%5Cfrac%7Ba%20%2A%20L%7D%7Bg%7D%20%3D%20%5Cfrac%7B8.08e-5%20%2A%200.75%7D%7B9.81%7D%20%3D%206.18e-6%20m%20%3D%206.18%20um)
The statement given in the question is FALSE.
Ecological Succession refers to the change in the specie structure of an ecosystem over a long period of time. There are two types of succession, primary and secondary succession. A primary success is said to occur when an ecosystem is totally destroyed to the extent that even the soil is wipe out. In this case, the ecosystem development has to start from the scratch. A succession is said to secondary if only part of the ecosystem is destroyed.
Answer:
12 meters per seconds......
Explanation:
60/5=12
Answer:
b. The voltage across the resistor is equal to the terminal voltage of the battery, and the voltage across the capacitor is zero.
Explanation:
<em>When the system reaches its steady state the current tends to zero, then</em>
<em>in the resistor</em>
<em>V=IR</em>
<em>I=0, then </em><em>V=0</em>
<em>the capacitor charged is like an interruption in the circuit. </em><em>If we mesure voltage on both sides of the battery and if we mesure both sides of the capacitor, we will get the same value</em><em>, as its not any component between them in one side, and, in the other, the only component is the resistor that, without any courrent doesn't discipates any energy.</em>
Answer:
add new genes to a gene pool