While 75-kg Anthony roller skates at 3 m/s, 60-kg Sue jumps into his arms with a velocity of 5 m/s. How fast does the pair go to
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This question is incomplete, the complete question is;
A high-resistance material is used as an insulator between the conductors of a length of coaxial cable. The resistance material, which forms a hollow tube, has an inner radius a and an outer radius b, and the insulator provides a resistance R between the conductors. If a second insulator, made of the same material and having the same length, is made with double both the inner radius and the outer radius of the first, what resistance would it provide between the conductors
a) (In2)R
b) 4R
c) R/(In2)
d) 2R
e) R
Answer: Option e) R is the correct answer.
Explanation:
Given that;
Inner radius = a
Outer radius = b
Conical Cylinder
∫dR = ∫(edr/2πrL)
R = e/2πL In e |ᵇₐ
R = e/2πL In(b/a) ------------- let this be equation 1
Taking a look at the second cone
a' = 2a
b' = 2a
R' = e/2πL In(2b/2a)
{L = L'}
R' = e/2πL In(b/a) -------let this be equation 2
now lets compare the two equation
R = e/2πL In(b/a)
R' = e/2πL In(b/a)
so R' = R
Therefore Option e) R is the correct answer.
Wave An oscillation that transfers energy and momentum.
Mechanical wave A disturbance of matter that travels along a medium. Examples include waves on a string, sound, and water waves.
Wave speed Speed at which the wave disturbance moves. Depends only on the properties of the medium. Also called the propagation speed.
Transverse wave Oscillations where particles are displaced perpendicular to the wave direction.
Longitudinal wave Oscillations where particles are displaced parallel to the wave direction.
In a transverse wave, perpendicular to the direction the wave travels, the particles are displaced. Examples of transverse waves include on a string vibrations and on the water surface ripples. By moving the slinky up and down vertically, we can create a horizontal transverse wave.
In a longitudinal wave, parallel to the direction the wave travels, the particles are displaced. Compressions that move along a slinky are an example of longitudinal waves. By pushing and pulling the slinky horizontally, we can make a horizontal longitudinal wave.
Common mistakes and misconceptions
Sometimes people forget that wave velocity is not the same as the velocity of the medium particles. How fast the disturbance travels through a medium is the wave speed. The velocity of the particle is how fast a particle moves about its position of equilibrium.
