How could you increase the air pressure inside a bag contaning a group of air molecules?

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

4 years ago

How do you solve for frequency?

AleksAgata [21]

Answer:

frequency= 1/time period

5 0

3 years ago

Which situation is an example of increasing potential energy? Question 4 options: A. a cat jumping from a tree B. pulling a wago

jeka94

Pulling an wagon uphill I believe.

4 0

3 years ago

Read 2 more answers

At its widest point, the diameter of a bottlenose dolphin is 0.50 m. Bottlenose dolphins are particularly sleek, having a drag c

fiasKO [112]

Answer:

497.00977 N

3742514.97005

Explanation:

$\rho$ = Density of water = 1000 kg/m³

C = Drag coefficient = 0.09

v = Velocity of dolphin = 7.5 m/s

r = Radius of bottlenose dolphin = 0.5/2 = 0.25 m

A = Area

Drag force

$F_d=\frac{1}{2}\rho CAv^2\\\Rightarrow F_d=\frac{1}{2}\times 1000 \times 0.09(\pi 0.25^2)7.5^2\\\Rightarrow F_d=497.00977\ N$

The drag force on the dolphin's nose is 497.00977 N

at 20°C

$\mu$ = Dynamic viscosity = $1.002\times 10^{-3}\ Pas$

Reynold's Number

$Re=\frac{\rho vd}{\mu}\\\Rightarrow Re=\frac{1000\times 7.5\times 0.5}{1.002\times 10^{-3}}\\\Rightarrow Re=3742514.97005$

The Reynolds number is 3742514.97005

8 0

3 years ago

A molecular cloud fragments as it collapses because Choose one: A. the interstellar wind is stronger in some places than others.

kondaur [170]

The cause for a molecular cloud forming fragments when it collapses is indicated correctly by option D. density variations from place to place grow larger as the cloud collapses.

Molecular cloud:

A molecular cloud, also known as a stellar nursery, is a specific kind of interstellar cloud, whose density and size allow the development of molecules, absorption nebulae, and H II regions. In contrast, some regions of the interstellar medium mostly consist of ionized gas.

Molecular clouds are cold, dense areas of space where stars form. The cloud collapses into a proto-star when the gravitational force pulling it in outweighs the internal pressure pushing it in.

When a molecular cloud collapses, it is observed that the density varies from place to place with the variation increasing with collapse. As a result, the collapse is characterized by fragmentation of the cloud.

Thus the correct option is: D. density variations from place to place grow larger as the cloud collapses.

Learn more about molecular clouds,

brainly.com/question/3459894

#SPJ4

6 0

2 years ago