Answer:
1.
2.
3.The results from part 1 and 2 agree when r = R.
Explanation:
The volume charge density is given as

We will investigate this question in two parts. First r < R, then r > R. We will show that at r = R, the solutions to both parts are equal to each other.
1. Since the cylinder is very long, Gauss’ Law can be applied.

The enclosed charge can be found by integrating the volume charge density over the inner cylinder enclosed by the imaginary Gaussian surface with radius ‘r’. The integration of E-field in the left-hand side of the Gauss’ Law is not needed, since E is constant at the chosen imaginary Gaussian surface, and the area integral is

where ‘h’ is the length of the imaginary Gaussian surface.

2. For r> R, the total charge of the enclosed cylinder is equal to the total charge of the cylinder. So,

3. At the boundary where r = R:

As can be seen from above, two E-field values are equal as predicted.
Answer:
The basic construction, unchanged since Torricelli's experiment in 1643, is a glass tube about three feet long, closed at one end, filled with mercury, and inverted with the open end immersed in a cistern of mercury.
Answer:
C) 20 m/s
Explanation:
Wave: A wave is a disturbance that travels through a medium and transfers energy from one point to another, without causing any permanent displacement of the medium itself. Examples of wave are, water wave, sound wave, light rays, radio waves. etc.
The velocity of a moving wave is
v = λf ............................ Equation 1
Where v = speed of the wave, λ = wave length, f = frequency of the wave.
Given: f = 2 Hz (two complete cycles in one seconds), λ = 10 meters
Substituting these values into equation 1
v = 2×10
v = 20 m/s.
Thus the speed of the wave = 20 m/s
The right option is C) 20 m/s