Answer:
I(x) = 1444×k ×
I(y) = 1444×k ×
I(o) = 3888×k ×
Explanation:
Given data
function = x^2 + y^2 ≤ 36
function = x^2 + y^2 ≤ 6^2
to find out
the moments of inertia Ix, Iy, Io
solution
first we consider the polar coordinate (a,θ)
and polar is directly proportional to a²
so p = k × a²
so that
x = a cosθ
y = a sinθ
dA = adθda
so
I(x) = ∫y²pdA
take limit 0 to 6 for a and o to
for θ
I(x) =
y²p dA
I(x) =
(a sinθ)²(k × a²) adθda
I(x) = k
da ×
(sin²θ)dθ
I(x) = k
da ×
(1-cos2θ)/2 dθ
I(x) = k
×
I(x) = k ×
× (
I(x) = k ×
×
I(x) = 1444×k ×
.....................1
and we can say I(x) = I(y) by the symmetry rule
and here I(o) will be I(x) + I(y) i.e
I(o) = 2 × 1444×k ×
I(o) = 3888×k ×
......................2
Hold on and let's discuss this realistically.
Because of gravity, there are two forces between the Earth and me. One draws me toward the Earth. The strength of that force is what I call my "weight". The other force draws the Earth toward me, and has the same strength.
The strength of these forces depends on the masses of the Earth and me. If the strength just tripled, that means that at least one of us just picked up a lot more mass. If the Earth suddenly became three times as massive, then the weight of everything and everybody on it would suddenly triple, and I'm pretty sure it would be the end of all of us before too long.
If it was only MY mass that suddenly tripled, that would mean that I had gone tearing through my house and the neighbour's house, eating everything in sight including the 2 couches, 3 dogs, and 6 TVs. Naturally, just as you would expect, my weight changed from 207 to 621, and my skin is stretched really tight.
ooohhh
Here, as the charge is uniformly distributed in the sphere, we will consider s as an area of the sphere which is, s=4πr2 and r is radius of the gaussian surface shown in the figure above. From this, it can be seen that
Answer:
When the magnetic field is tilted so it is no longer perpendicular to the page.
When the magnetic field gets stronger.
When the size of the loop decreases.
Explanation:
According to the Faraday-Lenz law, the change of the magnetic flux over time causes an induced current, this flux is given by:

Therefore, there will be a variable magnetic flux, when the magnitude of the magnetic field (B) changes over time, when the area of the loop (S) changes over time and / or when the angle (
) between the field and the surface vector changes over time.
Answer:
The value of current generated would increase.
Explanation:
Electromagnetic induction is the process by which an electromotive force is induced due to a variation of magnetic field.
The induced current is directly proportional to rate at which the coil cuts the magnetic field. Using more powerful battery in the experiment would increase the rate at the the coil cuts the magnetic field, therefore increasing the rate of variation in the magnetic field. This effect would cause a greater deflection on the galvanometer's scale, showing an increase in the current generated.
This experiment proves that an alternating current can be produced from magnetic field.