Answer:
4/10 of L.
Explanation:
A stopped pipe is a pipe with one closed end and one opened end. it is also called a closed pipe.
The fundamental mode of a stopped pipe is also called its fundamental frequency, and is f₁=v/4L.
Where f₁=fundamental frequency, v= velocity of sound, L= Length of pipe.
The fifth harmonic of the stopped pipe f₅ =5v/4L .................(1)
For an open pipe,
Fundamental mode is also called fundamental frequency f₁₀=v/2l₀ .......... (2)
Where f₁₀ = fundamental frequency of a closed pipe, v= velocity of sound and l₀=length of the resulting open pipe.
from the question, the fundamental mode of the resulting open pipe = The fifth harmonic of the original stopped pipe.
∴ f₅=f₁₀
⇒5v/4L = v/2l₀
Equating v from both side of the equation,
⇒ 5/4L = 1/2l₀
Cross multiplying the equation,
5×2l₀ = 4L× 1
10l₀ = 4L
Dividing both side of the equation by the coefficient of l₀ i.e 10
10l₀/10 = 4L/10
∴ l₀ = 4/10(L)
∴ 4/10 of L must be cut off
Answer:
Explanation:
We define the linear density of charge as:

Where L is the rod's length, in this case the semicircle's length L = πr
The potential created at the center by an differential element of charge is:

where k is the coulomb's constant
r is the distance from dq to center of the circle
Thus.

Potential at the center of the semicircle
Answer:
Option b
Explanation:
Metamorphism is the process where the variation of the geological texture resulting from the different arrangement of the minerals or the variation of minerals in protoliths, i.e., pre- existing rocks take place such that there occurs no change in state of the protolith, i.e., it does not melt into magma.
The change takes place as a result of the presence of chemically active fluids, heat and pressure.
There is a reaction between the chemically active fluid and the rock through which it passes and promotes the movement of the dissolved ions of silicate and promotes the growth of the mineral grains.
Answer:
The distribution is as depicted in the attached figure.
Explanation:
From the given data
- The plane wall is initially with constant properties is initially at a uniform temperature, To.
- Suddenly the surface x=L is exposed to convection process such that T∞>To.
- The other surface x=0 is maintained at To
- Uniform volumetric heating q' such that the steady state temperature exceeds T∞.
Assumptions which are valid are
- There is only conduction in 1-D.
- The system bears constant properties.
- The volumetric heat generation is uniform
From the given data, the condition are as follows
<u>Initial Condition</u>
At t≤0

This indicates that initially the temperature distribution was independent of x and is indicated as a straight line.
<u>Boundary Conditions</u>
<u>At x=0</u>
<u />
<u />
This indicates that the temperature on the x=0 plane will be equal to To which will rise further due to the volumetric heat generation.
<u>At x=L</u>
<u />
<u />
This indicates that at the time t, the rate of conduction and the rate of convection will be equal at x=L.
The temperature distribution along with the schematics are given in the attached figure.
Further the heat flux is inferred from the temperature distribution using the Fourier law and is also as in the attached figure.
It is important to note that as T(x,∞)>T∞ and T∞>To thus the heat on both the boundaries will flow away from the wall.
Answer:
In the case of a solution transition metal complex that has an absorption peak at 450 nm in the blue region of the visible spectrum, the (complementary) color of this solution is orange (option B).
Explanation:
The portion of UV-visible radiation that is absorbed implies that a portion of electromagnetic radiation is not absorbed by the sample and is therefore transmitted through it and can be captured by the human eye. That is, in the visible region of a complex, the visible color of a solution can be seen and that corresponds to the wavelengths of light it transmits, not absorbs. The absorbing color is complementary to the color it transmits.
So, in the attached image you can see the approximate wavelengths with the colors, where they locate the wavelength with the absorbed color, you will be able to observe the complementary color that is seen or reflected.
<u><em>
In the case of a solution transition metal complex that has an absorption peak at 450 nm in the blue region of the visible spectrum, the (complementary) color of this solution is orange (option B).</em></u>