A thin, uniform rod has length L and mass M. A small uniform sphere of mass m is placed a distance x from one end of the rod, along the axis of the rod.
a) Calculate the gravitational potential energy of the rod-sphere system. Take the potential energy to be zero when the rod and sphere are infinitely far apart. (Hint: Use the power series expansion for ln(1+x).)
b) Use Fx=−dU/dx to find the magnitude of the gravitational force exerted on the sphere by the rod.

Answers

Answer 1

Answer:

Explanation:

From the given information:

a)

Let's have an imaginary view of the rod located at a given distance r from he the mass (m) of the sphere.

Then the equation for the potential energy as related to the small area of the dr of the rod can be computed as:

[tex]dU = -\dfrac{GMm}{L}*\dfrac{dr}{r}[/tex]

where,

G = gravitational constant

[tex]U = - \int^{x+L}_{x}Gm\dfrac{M}{L}*\dfrac{dr}{r}[/tex]

[tex]U = - \dfrac{GMm}{L}\int^{x+L}_{x}\dfrac{dr}{r}[/tex]

By taking the integral within the limit

[tex]U = - \dfrac{GMm}{L} \Big[In \ r\Big]^{x+L}_{x}[/tex]

[tex]\mathbf{\implies - \dfrac{GmM}{L} In \Big(\dfrac{{x+L}}{{x}}\Big)}[/tex]

b)

By using [tex]F= -\dfrac{dU}{dx}[/tex], the magnitude of the gravitational force can be determined as follows:

Here, we have:

[tex]F = -\dfrac{d}{dx} \Big [\dfrac{-GmM}{L}In(\dfrac{x+l}{x}) \Big ] \\ \\ = \dfrac{GmM}{L}\times \dfrac{x}{x+L}\times (0-\dfrac{L}{x^2}) \\ \\ By \ solving \\ \\ \mathbf{ =-\dfrac{GmM}{x(x+L)}}[/tex]

From above, the negative sign indicates an attractive force


Related Questions

1. What are Earth's natural climate cycles?

Answers

The Earth's natural climate cycle
Over the last 800,000 years, there have been natural cycles in the Earth's climate. There have been ice ages and warmer interglacial periods. After the last ice age 20,000 years ago, average global temperature rose by about 3°C to 8°C, over a period of about 10,000 years.

A vessel at rest at the origin of an xy coordinate system explodes into three pieces. Just after the explosion, one piece, of mass m, moves with velocity (-21 m/s) and a second piece, also of mass m, moves with velocity (-21 m/s) . The third piece has mass 3m. Just after the explosion, what are the (a) magnitude and (b) direction (as an angle relative to the x axis) of the velocity of the third piece

Answers

Answer:

25

Explanation:

magnitude and (b) direction (as an angle relative to the x axis) of the velocity

At 20 ◦C a copper wire has a resistance of 4×10−3 Ω and a temperature coefficient of resistivity of 3.9×10−3 (C◦)−1, its resistance at 100 ◦C is

A.
52.5 × 10-3 Ω
B.
5.25 × 10-3 Ω
C.
5.25 × 10-4 Ω
D.
5.25 × 10-2 Ω


E.
25.5 × 10-3 Ω

Answers

Answer:

[tex]R _{t} = R _{0}( \alpha t + 1) \\ = 4 \times {10}^{ - 3} (3.9 \times {10}^{ - 3} \times 20 + 1) \\ = 4 \times {10}^{ - 3} (1.078) \\ = 4.312 \times {10}^{ - 3} \: Ω[/tex]

Compare the freezing point of water in the aquanaut’s apartment to its value at the surface. Is it higher, lower, or the same?

Answers

Answer:

Freezing Point - Lower

Boiling Point - Higher

Solid- liquid transition line in the phase diagram has a negative slope, but the liquid-gas transition line has a positive slope. Since there is more air pressure at 100m it will take less to freeze the water but more to boil it since it requires a larger temperature under larger pressures

the magnitude of the electrical force acting between a +2.4x10-8c charge and 1+1.8x10-6 charge that are separated by 1.008m is

Answers

Answer:

3.83×10¯⁴ N

Explanation:

From the question given above, the following data were obtained:

Charge 1 (q₁) = +2.4x10¯⁸ C

Charge 2 (q₂) = +1.8x10¯⁶ C

Distance apart (r) = 1.008 m

Electrical constant (K) = 9×10⁹ Nm²/C²

Force (F) =?

The magnitude of the electrical force acting between the two charges can be obtained as follow:

F = Kq₁q₂ / r²

F = 9×10⁹ × 2.4x10¯⁸ × 1.8x10¯⁶ / (1.008)²

F = 0.0003888 / 1.016064

F = 3.83×10¯⁴ N

Thus the magnitude of the electrical force acting between the two charges is 3.83×10¯⁴ N

violations in a responsible manner in a democratic society?
Activity 5:
Ending
From your findings, what conclusions and recommendations can you make on the
issue of human rights violations to:
5.1
Government​

Answers

Answer:

Kindly check explanation

Explanation:

The trampling and violation of human rights individuals, groups and corporate organizations is really alarming ad as such, the government who are charged to protect the right and interest of its citizen. In other to curtail the trending issues of human right violation, it is imperative if sensitization programmes could be organiz d in other to keep people informed of the various ways in which people's right may be trampled upon. With these education, the ignorance can be expunged leaving only those who genuinely decides to relate and threaten the right of his fellow country person.

The laws on human right violation should be reviewed and capital punishment metted on violators in other to send a strong warning to those who still nurture the intention.

PLEASE HELP ME WITH THIS ONE QUESTION
The color orange has a wavelength of 590 nm. What is the energy of an orange photon? (h = 6.626 x 10^-19, 1 eV = 1.6 x 10^-19 J)

A) 2.81 eV

B) 3.89 eV

C) 2.10 eV

D) 2.78 eV

Answers

The color orange has a wavelength of 590 nm. The energy of an orange photon is approximately 0.337 eV.

The correct answer is option E.

To calculate the energy of a photon, we can use the equation:

E = (hc) / λ

where E is the energy of the photon, h is the Planck's constant (6.626 x [tex]10^-^3^4[/tex]J·s or 6.626 x[tex]10^-^1^9^[/tex] eV·s), c is the speed of light (3.00 x [tex]10^8[/tex] m/s), and λ is the wavelength of the light.

Given that the wavelength of orange light is 590 nm (or 590 x [tex]10^-^9[/tex]m), we can substitute the values into the equation:

E = [(6.626 x[tex]10^-^1^9^[/tex] eV·s) x (3.00 x [tex]10^8[/tex] m/s)] / (590 x[tex]10^-^9[/tex]m)

E = (1.9878 x [tex]10^-^1^0[/tex]eV·m) / (590 x [tex]10^-^9[/tex] m)

E = 3.3695 x [tex]10^-^1[/tex] eV

For more such information on: wavelength

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The question probable may be:

The color orange has a wavelength of 590 nm. What is the energy of an orange photon? (h = 6.626 x [tex]10^-^1^9^[/tex], 1 eV = 1.6 x[tex]10^-^1^9^[/tex]J)

A) 2.81 eV

B) 3.89 eV

C) 2.10 eV

D) 2.78 eV

E)  0.337 eV

A rock is thrown from the top of a building 146 m high, with a speed of 14 m/s at an angle 43 degrees above the horizontal. When it hits the ground, what is the magnitude of its velocity (i.e. its speed).

Answers

Answer:

time is 32 s and speed is 304.3 m/s

Explanation:

Height, h = 146 m

speed, u = 14 m/s

Angle, A = 43 degree

Let it hits the ground after time t.

Use second equation of motion

[tex]h = u t +0.5 at^2\\\\- 146 =14 sin 43 t - 4.9 t^2\\\\4.9 t^2 - 9.5 t - 146 =0 \\\\t =\frac{9.5\pm\sqrt {90.25 + 2861.6}}{9.8}\\\\t=\frac{9.5\pm 54.3}{9.8}\\\\t = 32.05 s, - 22.4 s[/tex]

Time cannot be negative so the time is t = 32 s .

The vertical velocity at the time of strike is  

v' =  u sin A - g t

v' = 14 sin 43 - 9.8 x 32 = 9.5 - 313.6 = - 304.1 m/s

horizontal velocity

v'' = 14 cos 43 =10.3 m/s

The resultant velocity at the time of strike is

[tex]v=\sqrt{v'^2 + v''^2}\\\\v = \sqrt{304.1^2 +10.3^2 }\\\\v = 304.3 m/s[/tex]  

g is incident on 3 successive sheets of polarizing material. The transmission axis of the first sheet is vertical. The transmission axis of the second sheet is at 30 degrees from vertical. The transmission axis of the third is horizontal. What is the intensity of the light emerging from the third sheet

Answers

Answer:

The intensity of light passing from the third polarizer is 3Io/16.

Explanation:

The law of Malus is given by

[tex]I=I_o cos^2\theta[/tex]

Let the incident intensity of light is Io.

The intensity of light passing from the first polarizer is

[tex]I' = \frac{I_o}{2}[/tex]

The intensity of light passing from the second polarizer is

[tex]I''=\frac{I_o}{2}\times cos^230 =\frac{3I_o}{8}[/tex]

The intensity of light passing from the third polarizer is

[tex]I''' = \frac{3I_o}{8}\times cos^2 60\\\\\\I''' = \frac{3I_o}{16}[/tex]

what happened on march 21 every year in the northern hemisphere​

Answers

Answer:

B. The Spring equinox

Explanation:

The vernal equinox marks the moment the sun crosses the celestial equator.  The vernal equinox happens on March 19, 20, or 21 every year in the Northern Hemisphere. In the Southern Hemisphere, this same event marks the beginning of fall.  (Source: What Exactly Is The Spring Equinox? - Dictionary.com)

Hopefully this helps.

Which statement describes an action-reaction pair?
O A. You push on a car, and the car pushes back on you.
B. A book pushes down on a table, and the table pushes down on the
Earth.
C. The Moon pulls on Earth, and Earth pulls on the Sun.
D. You push down on your shoe, and Earth's gravity pulls down on the
shoe.

Answers

Answer:

A

Explanation:

a pex

The current through a 3.0 Ω resistor is 0.30 A. The resistor is wired in series with a 9.0 V battery and an unknown resistor. What is the value of the unknown resistor?

Answers

Answer:

answer is 37 ohm since current e

remains same in series

Find the ratio of speeds of an electron and a negative hydrogen ion (one having an extra electron) accelerated through the same voltage, assuming non-relativistic final speeds. Take the mass of the hydrogen ion to be 6.7 X 10 -27 Kg.

Answers

Answer:

 v₂ /v₁ = 2.3 10⁺²

Explanation:

The energy is conserved so the total potential energy must be transformed into kinetic energy

          K = U

          ½ m v² = q ΔV

          v = [tex]\sqrt{\frac{2q \Delta V}{m} }[/tex]

a) Let's find the speed of the electron

           m = 9.1 10⁻³¹ kg

as they do not indicate the value of the power difference, we will assume that ΔV = 1 V is worth one

           v = [tex]\sqrt{ \frac{2 \ 1.6 \ 10^{-19} \ 1}{9.1 \ 10^{-31}} }[/tex]

           v = [tex]\sqrt {0.3516 \ 10^{12}}[/tex]

           v1 = 0.593 10⁶ m / s

b) the velocity of a hydrogen ion

            M = M_H + m

            M = 1.673 10⁻²⁷ + 9.1 10⁻³¹

            M = 1.67391 10⁻²⁷ kg

            M = 1.67 10⁻²⁷ kg

            v = [tex]\sqrt{ \frac { 2 \ 1.6 \ 10^{-19} \ 1}{1.67 \ 10^{-27}} }[/tex]

             v = [tex]\sqrt{ 1.916167 \ 10^8 }[/tex]

             v₂ = 1.38 10⁴ m / s

the relationship between these speeds is

           v₂ / v₁ = 1.38 10⁴ / 0.593 10⁶

           v₂ /v₁ = 2.3 10⁺²

can anyone explain soil erosion

Answers

Answer:

Soil erosion is the act of removing the top layer of the soil either by rain wind or human activities

Answer:

l erosion is a gradual process that occurs when the impact of water or wind detaches and removes soil particles, causing the soil to deteriorate. ... The impact of soil erosion on water quality becomes significant, particularly as soil surface runoff. Sediment production and soil erosion are closely related.

Explanation:

The momentum of a falling rock is found to be 200 kg m/s. What is the mass of the rock if it falls with a velocity of 5.0 m/s

Answers

Answer:

[tex]\boxed {\boxed {\sf 40 \ kilograms}}[/tex]

Explanation:

Momentum is the product of velocity and mass. The formula is:

[tex]p=m*v[/tex]

We know the rock is falling. Its momentum is 200 kilograms meters per second and its velocity is 5 meters per second. Substitute the values into the formula.

[tex]200 \ kg \ m/s = m * 5.0 \ m/s[/tex]

We are solving for m, the mass. We must isolate the variable. It is being multiplied by 5 meters per second. The inverse of multiplication is division, so we divided both sides by 5.0 m/s.

[tex]\frac{200 \ kg \ m/s}{5.0 \ m/s}=\frac{ m* 5.0 \ m/s }{5.0 \ m/s}[/tex]

[tex]\frac{200 \ kg \ m/s}{5.0 \ m/s}=m[/tex]

The units of meters per second (m/s) cancel.

[tex]\frac{200 \ kg}{5.0 } =m[/tex]

[tex]40 \ kg = m[/tex]

The falling rock has a mass of 40 kilograms.

Select the correct answer.
If you increase the frequency of a sound wave four times, what will happen to its speed?
A.
The speed will increase four times.
B.
The speed will decrease four times.
C.
The speed will remain the same.
D.
The speed will increase twice.
E.
The speed will decrease twice.

Answers

Answer:

A. The speed of the wave increases four times.

Answer:

A. The speed will increase four times.

Explanation:

If you increase the frequency of a sound wave four times, the speed will increase four times. So, option (A) is correct.

A professional quarterback throws a 0.40 kg football. what is the force of weight?

Answers

Answer:

3.92N

Explanation:

Force= mass×accelerarion due gravity

But mass= 0.40kg

acceleration due to gravity = 9.8 m/s^2

Force = 0.40×9.8

Force=3.92N

En 2.0 s, una particula con aceleración constante a lo largo del eje x se mueve desde x =10 m
hasta x =50 m. La rapidez al final del recorrido es de 10 m/s. ¿Cuál es la aceleración de la partícula?

Answers

The correct response is x23

Speeding up


Slowing down


Standing still


Holding at a constant non-zero velocity

Answers

Answer:

speeding up is the answer

Explanation:

from the graph it can be seen that as the time (horizontal axis) increases the speed of vehicle (vertical axis) increases

What are the practical systems under continuos time system?​

Answers

Answer:

REVIEWS

Wing-Kuen Ling, in Nonlinear Digital Filters, 2007

Controllability and observability

For a continuous time system, assume that x(0) = 0. ∀x1, if ∃t1 > 0 and u(t) such that x(t1) = x1, then the continuous time system is said to be reachable. Similarly, for a discrete time system, assume that x(0) = 0. ∀x1, if ∃n1 > 0 and u(n) such that x(n1) = x1, then the discrete time system is said to be reachable. For a continuous time system, if ∀x0, x1, ∃t1 > 0 and u(t) such that x(0) = x0 and x(t1) = x1, then the continuous time system is said to be controllable. Similarly, for a discrete time system, if ∀x0, x1, ∃n1 > 0 and u(n) such that x(0) = x0 and x(n1 = x1, then the discrete time system is said to be controllable. For LTI systems, the set of reachable state is R(|BAB… AnB|), where R(A) is defined as the range of A, that is R(A) = {y : y = Ax}. Also, the LTI systems are controllable if and only if R(A) = Rn Or in other words, rank(|BAB… AnB|) = n.

If we double the mass of an object without a change in volume, its density would be

A) half.
B) double.
C) unchanged.

Answers

The formula for density is
density
=
mass
volume
.
We need to double the volume, i.e. multiply it by
2
.
But in order to multiply one side of the equation by a number, the same has to be done to the other side.
Multiplying the volume by
2
is the same as multiplying the fraction
mass
volume
by
1
2
.
So let's multiply both sides of the equation by
1
2
:

1
2
×
density
=
1
2
×
mass
volume

density
2
=
mass
2
×
volume
Therefore, doubling the volume results in the density being halved.

Answer: Half


how to calculate sound of an echo ​

Answers

by an echo meter

please flw me and thank my answers

#Genius kudi

Some runners train with parachutes that trail behind them to provide a large drag force. These parachutes are designed to have a large drag coefficient. One model expands to a square 1.8 mm on a side, with a drag coefficient of 1.4. A runner completes a 240 mm run at 6.0 m/s with this chute trailing behind.

Required:
How much thermal energy is added to the air by the drag force?

Answers

Answer:

by the drag force, 2.4004512 × 10⁻⁵ J is added to the air.

Explanation:

Given the data in the question;

drag coefficient of Cd = 1.4

speed v = 6.0 m/s

One model expands to a square 1.8 mm on a side

Area A = 1.8 × 1.8 = 3.24 mm² = 3.24 × 10⁻⁶ m²

distance travelled s = 240 mm = 0.24 m

we know that; density of air e = 1.225 kg/m³

Now,

Dragging force F[tex]_D[/tex] = ( Cd × e × v² × A  ) / 2

thermal energy = F[tex]_D[/tex] × s

so

thermal energy = ( 1.4 × 1.225  × (6)² × (3.24 × 10⁻⁶) × 0.24  ) / 2

thermal energy = ( 4.8009024 × 10⁻⁵ ) / 2

thermal energy = 2.4004512 × 10⁻⁵ J

Therefore,  by the drag force, 2.4004512 × 10⁻⁵ J is added to the air.

A dog accelerates at 1.50 m/s2 to reach a velocity of 13.5 m/s while covering a distance of 49.3 m. What was his initial velocity?

Answers

Let v be the dog's initial velocity. Then

(13.5 m/s)^2 - v ^2 = 2 (1.50 m/s^2) (49.3 m)

==>   v ^2 = (13.5 m/s)^2 - 2 (1.50 m/s^2) (49.3 m)

==>   v = √((13.5 m/s)^2 - 2 (1.50 m/s^2) (49.3 m))

==>   v5.86 m/s

planet a takes one year to go around the sun at a distance of one au. .planet b is three a u. from the sun. how many years does planet b take to orbit?

Answers

Answer:

3 years

Explanation:

Find the circumference of each orbit in AU.

2xπx1=6.283185307

2xπx3=18.84955592

Divide them.

18.84955592/6.283185307=3

3 years

You want to calculate how long it takes a ball to fall to the ground from a
height of 20 m. Which equation can you use to calculate the time? (Assume
no air resistance.)
O A. vz? = v? +2aAd
B. a =
V₂-vi
At
O c. At=V1
4
a
O D. At=
2Ad
a

Answers

If a person wants to calculate the length of time it takes for a ball to fall from a height of 20m, the correct equation that they should use is:

D. Δt= √2Δd/a

What is the equation for finding the length of time for a free fall?

The free fall formula should be used to obtain the length of time that it takes for a ball to fall from a given height. This formula also factors the height or distance from which the fall occurred and this is denoted by the letter d. The small letter 'a' is denotative of acceleration due to gravity and this is a constant pegged at -9.98 m/s².

So, the change in height is obtained and multiplied by two. This is further divided by the acceleration and the square root of the derived answer translates to the time taken for the ball to fall from the height of 20m. Of all the options listed, option D represents the correct equation.

Learn more about free fall here:

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need in hurry please

Answers

Answer : C

Explanation: The object is the point where P and Q meet
Unlike linear vectors where they are just straight lines and you just add and subtract
This diagram is a 2D vector therefore the resultant is between line P Ana Q and the direction is pointing outward.

I hope this helps :)

Which type of energy is stored in a battery?
A. Nuclear energy
B. Electromagnetic energy
C. Chemical energy
D. Electrical energy
SUBMI

Answers

Answer:

c

Explanation:

in food and batteries chemical energy is stored :) hope this helped

A motor lifts a weight of 5N up to the height of 2m in 4 seconds. What will be the power of motor?​

Answers

2.5 watt

Explanation:

we know

power = work done /time

work done gainst gravity is = mgh

as mg = weight = force = 5 N

and height = 2 m

so work done = mgh = 5*2 = 10N

therefore ,

Power = 10/4 = 2.5 watt

Which statements describe using genetic factors to influence the growth of organisms? Select the three (3) that apply.
-increasing use of hybrid crops
-altering genes in DNA to create new plants
-increasing human population
-increasing climate change
-developing disease or pest resistant crops

Answers

Answer:

- increasing use of hybrid crops

- altering genes in DNA to create new plants

- developing disease or pest resistant crops

Explanation:

The use of genetic factors to influence the growth of a plant encompasses manipulating the genetic constituent (gene) of such plant.

For example,

- Increasing use of hybrid crops entails mating two pure bred plants based on a gene of interest responsible for a particular trait, to form a hybrid.

- Altering genes in DNA to create new plants is also a genetic factor as it has to with gene modification.

- developing disease or pest resistant crops means that the genetic make up of such plant has been modified to be resistant to pest/disease.

Other Questions
I'll give you more points but you have to answer all the parts to the question. I need this plsssss ty lol. Show all work too plssss. HELP ASAP PLEASE (1) In 1751, the Philadelphia Provincial Assembly had a bell made. (2) It was for the new State House. (3) The bell weighed more than 2,000 pounds. (4) The bell was 12 feet in circumference around the bottom. (5) It came to be known as the Liberty Bell because it was inscribed with a motto about liberty. (6) Unfortunately, the Liberty Bell cracked in 1752 during a test ring. (7) To fix the bell, the Philadelphia Assembly had it recast. (8) Some people say the bell cracked again in 1835. (9) It was tolling for John Marshalls funeral. (10) However, that is probably just a legend. (11) It is a fact that on February 22, 1846, the bell cracked again. (12) That crack could not be fixed. (13) The Liberty Bell has had a crack in it ever since.~ Which is the most effective way to combine sentences 3 and 4?1. More than 2,000 pounds and 12 feet in circumference around the bottom, the bell.2. The bell weighed more than 2,000 pounds and was 12 feet in circumference around the bottom.3. Weighing more than 2,000 pounds and 12 feet in circumference around the bottom was the Liberty Bell.4. The bell weighed more than 2,000 pounds, the bell was 12 feet in circumference around the bottom. Nicaragua is in Central America, with coasts on both the Pacific Ocean andthe Caribbean Sea. Most people in Nicaragua speak Spanish, and the majorityof people are of mixed ancestry (Native and European). Nicaragua is thepoorest country in Central America and the second poorest nation in theWestern Hemisphere. A long civil war and a major hurricane in 1998 hurt theeconomy, which is slowly being rebuilt.Which of the following facts from the paragraph above best describes anelement of Nicaragua's culture?A. A major hurricane struck the coast.B. It lies between the Pacific Ocean and the Caribbean Sea.C. It is one of the poorest countries in the Western Hemisphere.aD. Spanish is the main language. How does the geographic theme of location help us understand life on Earth?A. It tells us about people's migration to a region.B. It tells us what a region is like.O c. It tells us how people have affected the environment of a region.D. It tells us where to find a region. Choose the sentence that has correct capitalization.Let's work together on our algebra and english homework.Let's work together on our Algebra and English homework.Let's work together on our algebra and English homework. President Carters stimulus plans One thousand dollars is invested at 5% continuous annual interest. This means the value of the investment will grow exponentially, with k equaling the decimal rate of interest. What will the value of the investment be after 7 1/2 years The goal of vietnam war was to stop _______ from across southeast asiaA- capitalism B- communism C- fascismD- otherism ANSWER PLEASE!!!!!!!!!!!!! If a 60 W light bulb and a 75 W light bulb operate from 150 V source, which bulb has a greater current in it?60 W75 W When you accelerate, the size of the front tire patch becomes____ If I have a right triangle ab=12 and ac=15 what is BC 2x2-1/3x2+7/3x2 plzzzzzzzzzzzz fast A town meeting the mayor has presented several ways the town Could provide child care to families in which both parents work what should the participants at the meeting do next A. Hold elections for a new mayorB. Implement each of the new ways to see which one works best C. Evaluate how well that may your proposal worksD. Consider the cost and benefits of each way before choosing one Difference between d pharma and b pharma What did you notice about this poems structure as you listened? Check all that apply. Write an equation to match the situation below. Then, use your equation to solve for the variable.Haley received $278.25 in her paycheck for working h hours this week. She makes $13.25 per hour.I V. ASSESSMENT (Time Frame:(Learning Activity Sheets for Enrichment, Remediation, or Assessment to be givenDirection: Choose the letter of the correct answer. Use another1. These are materials or substances such as minerals, foreused for economic gain.A. Natural resourcesC. Non renewableB. Renewable resourcesD. Minerals2. In which way can we protect our environment?A. LitteringC. recyclingB. PollutingD. contaminating3. Which of these is the primary cause of land pollution?A. Improper garbage disposal C. Recycling mateB. Planting of treesD. Waste segrega4. Your community is rich in metallic materials. Which ofconserve such precious mineral deposits? Which multiplication problem is represented by the model?Divide. Write your answer in simplest form.1/5 4 Under what circumstance do we say two or more nodes are daughters of another node in P-marker?