Please answer correctly. Will give the brainliest !!! Urgent !!! Please help !!

Find the moments of inertia Ix, Iy, I0 for a lamina that occupies the part of the disk x2 y2 ≤ 36 in the first quadrant if the d

Tasya [4]

Answer:

I(x) = 1444×k × ${\pi}$

I(y) = 1444×k × ${\pi}$

I(o) = 3888×k × ${\pi}$

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 $\pi /2$ for θ

I(x) = $\int_{0}^{6}\int_{0}^{\pi/2}$ y²p dA

I(x) = $\int_{0}^{6}\int_{0}^{\pi/2}$ (a sinθ)²(k × a²) adθda

I(x) = k $\int_{0}^{6}a^(5)$ da × $\int_{0}^{\pi/2}$ (sin²θ)dθ

I(x) = k $\int_{0}^{6}a^(5)$ da × $\int_{0}^{\pi/2}$ (1-cos2θ)/2 dθ

I(x) = k $({r}^{6}/6)^(5)_0$ × ${θ/2 - sin2θ/4}^{\pi /2}_0$

I(x) = k × $({6}^{6}/6)$ × ( ${\pi /4} - sin\pi /4)$

I(x) = k × $({6}^{5})$ × ${\pi /4}$

I(x) = 1444×k × ${\pi}$ .....................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 × ${\pi}$

I(o) = 3888×k × ${\pi}$ ......................2

3 0

3 years ago

The volume of a gas depends upon its mass true or false

Kruka [31]

I would say false because the volume of gas depends on several things the amount of matter in the volume , the pressure and the temperature. So the answer would be false in my opinion. Because mass is not the only factor

4 0

3 years ago

A system expands from a volume of 1.00 l to 2.00 l against a constant external pressure of 1.00 atm. what is the work (w) done b

stepan [7]

The work done by a system kept at constant pressure is given by:
$W=p \Delta V = p (V_f - V_i)$
where
p is the pressure
$V_f$ is the final volume
$V_i$ is the initial volume

If we plug the numbers given by the problem into this equation, we find
$W=p (V_f -V_i)=(1.00 atm)(2.00 L-1.00 L)=1.00 L\cdot atm$

And since $1 atm \cdot L = 101.3 J$ , we have that the work done is
$W= 1.00 atm \cdot L = 101.3 J$

8 0

3 years ago

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URGENT HELP PLEASE, GIVING BRAINLIEST IF YOU ANSWER CORRECTLY!! (20 pts!!)

Kobotan [32]

The answer is c 1386j

This calculator is very helpful I use it on my homework

https://www.omnicalculator.com/physics/specific-heat

8 0

3 years ago

A student places four identical cells into four different liquids. Cell Description of Liquid W Saltier than the cell X Less sal

Tems11 [23]

This description can be expressed as follows:

$Y>W>X$

And,

$W=Z$

From these expressions we are able to find out that the saltiest cell description is Y, while the less salty is X.

Now, salt is well known as a dehydrating agent. In a process called osmosis cells placed in a salty liquid environment lose water, how?

Well, cells have a semipermeable membrane, in which some substances can get inside. Cells also have water inside. If a cell is placed in a quite salty liquid environment, salt will make the water inside the cells to come out, drying the cell and diminishing its size.

So, in this case, according to the expressions above, Cell Y will look the smallest, while cell X will look the biggest.

If we pour pure water in each liquid, the salt concentration will change and each cell will begin to grow bigger, but the saltiest cell will still be smaller than the others with less salt concentration.

Finally, to answer the question: Y cell will look the smallest after this process.

8 0

3 years ago

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