Ask question

Ask question

All categories

3 years ago

13

A spherical shell has an outside radius of 2.60 cm and an inside radius of a. The shell wall has uniform thickness and is made o

f a material with density 4.70 g/cm3. The space inside the shell is filled with a liquid having a density of 1.23 g/cm3. (a) Find the mass m of the sphere, including its contents, as a function of a. (b) In the answer to part (a), if a is regarded as a variable, for what value of a does m have its maximum possible value

1 answer:

lbvjy [14]3 years ago

4 0

Answer:

The answer is below

Explanation:

a) The volume of a sphere is:

Volume = (4/3)πr³; where r is the radius of the shell.

Given the outside radius of 2.60 cm and inner radius of a cm, the volume of the spherical shell is:

Volume of spherical shell = $\frac{4}{3} \pi (2.6^3-a^3)$ cm³

But Density = mass / volume; Mass = density * volume.

Therefore, mass of spherical shell = density * volume

mass of spherical shell = $4.70\ g/cm^3$ * $\frac{4}{3} \pi (2.6^3-a^3)$ cm³

Mass of liquid = volume of inner shell * density of liquid

Mass of liquid = $\frac{4}{3} \pi a^3\ cm^3*1.23\ g/cm^3$

Total mass of sphere including contents = mass of spherical shell + mass of liquid

Total mass of sphere including contents (M) = $4.70\ g/cm^3$ * $\frac{4}{3} \pi (2.6^3-a^3)\ cm^3$ + $\frac{4}{3} \pi a^3\ cm^3*1.23\ g/cm^3$ =

Total mass of sphere including contents (M) = (346 - 14.5a³) grams

b) The mass is maximum when the value of a = 0

M = 346 - 14.5a³

M' = 43.5a² = 0

43.5a² = 0

a = 0

You might be interested in

What does it mean to say that current and resistance in a circuit are inversely related?

Kobotan [32]

As the resistance increase the current decreases and vice versa

7 0

4 years ago

The ________ on the axis (c2) forms a pivot point with the atlas (c1) that allows you to nod a "no."

strojnjashka [21]

The dens or the odontoid process of the axis or the second cervical spine forms a pivot point with the atlas or the first cervical vertebrae that is responsible for the nodding and the rotational movements of the head. This is reinforced by ligaments and the atlanto-occipital joint that allows the head to make a nodding or up and down movement on the vertebral column.

3 0

3 years ago

Consider the possible scenarios and determine which of them are true for positive feedbacks or negative feedbacks.A. Increased p

avanturin [10]

Answer:

Scenario A, B and E is True.

Explanation:

Scenario A) True. Removing carbon dioxide from atmosphere decreases greenhouse effect of atmosphere. Thus, temperature rise decreases.

Scenario B) True. The more evaporation creates the more greenhouse effect. Therefore, temperature rise increases.

Scenario C) False. Removing carbon dioxide from atmosphere decreases greenhouse effect of atmosphere. Thus, temperature rise decreases.

Scenario D) False. The more evaporation creates the more greenhouse effect. Therefore, temperature rise increases.

Scenario E) True. If reflected radiation increases from Earth, temperature rise of the Earth will decrease. Ice cover increases reflectivity which leads temperature level decrease.

Scenario F) False. If reflected radiation increases from Earth, temperature rise of the Earth will decrease. Ice cover increases reflectivity which leads temperature level decrease.

5 0

4 years ago

The Moon requires about 1 month (0.08 year) to orbit Earth. Its distance from us is about 400,000 km (0.0027 AU). Use Kepler’s t

dem82 [27]

Answer:

$\frac{M_e}{M_s} = 3.07 \times 10^{-6}$

Explanation:

As per Kepler's III law we know that time period of revolution of satellite or planet is given by the formula

$T = 2\pi \sqrt{\frac{r^3}{GM}}$

now for the time period of moon around the earth we can say

$T_1 = 2\pi\sqrt{\frac{r_1^3}{GM_e}}$

here we know that

$T_1 = 0.08 year$

$r_1 = 0.0027 AU$

$M_e$ = mass of earth

Now if the same formula is used for revolution of Earth around the sun

$T_2 = 2\pi\sqrt{\frac{r_2^3}{GM_s}}$

here we know that

$r_2 = 1 AU$

$T_2 = 1 year$

$M_s$ = mass of Sun

now we have

$\frac{T_2}{T_1} = \sqrt{\frac{r_2^3 M_e}{r_1^3 M_s}}$

$\frac{1}{0.08} = \sqrt{\frac{1 M_e}{(0.0027)^3M_s}}$

$12.5 = \sqrt{(5.08 \times 10^7)\frac{M_e}{M_s}}$

$\frac{M_e}{M_s} = 3.07 \times 10^{-6}$

4 0

3 years ago

List two types. Of organelles

Helen [10]

Theres: the vacuole, nucleus, rough endoplamid reticulum, smooth endoplasmic reticulum, cell memebrane, cell wall, chloroplast, mitochondria, golgi apperatus, lysosomes, and ribosomes

6 0

3 years ago