Answer:
The induced emf is
Explanation:
From the question we are told that
The radius of the circular loop is 
The intensity of the wave is 
The wavelength is 
Generally the intensity is mathematically represented as

Here
is the permeability of free space with value

B is the magnetic field which can be mathematically represented from the equation as

substituting values


The area is mathematically represented as

substituting values


The angular velocity is mathematically represented as

substituting values
Generally the induced emf is mathematically represented as

At maximum induced emf 
So

substituting values
The correct choice is
D. 22 Hz and 42 Hz.
In fact, the beat frequency is given by the difference between the frequencies of the two waves:

In this problem, the beat frequency is
, therefore the only pair of frequencies that gives a difference equal to 20 Hz is
D. 22 Hz and 42 Hz.
Answer:
![r_{cm}=[12.73,12.73]cm](https://tex.z-dn.net/?f=r_%7Bcm%7D%3D%5B12.73%2C12.73%5Dcm)
Explanation:
The general equation to calculate the center of mass is:

Any differential of mass can be calculated as:
Where "a" is the radius of the circle and λ is the linear density of the wire.
The linear density is given by:

So, the differential of mass is:


Now we proceed to calculate X and Y coordinates of the center of mass separately:


Solving both integrals, we get:


Therefore, the position of the center of mass is:
![r_{cm}=[12.73,12.73]cm](https://tex.z-dn.net/?f=r_%7Bcm%7D%3D%5B12.73%2C12.73%5Dcm)