g the parallel axis theorem relates icm, the moment of inertia of an object about an axis passing through its center of mass, to ip, the moment of inertia of the same object about a parallel axis passing through point p. the mathematical statement of the theorem is ip

A projectile of mass m is fired horizontally from a height h above the level ground and with a speed v. solve for the following in terms of m, h, v, and appropriate constants. The work done by the projectile is 'mgh' and its kinetic energy will be  [tex]\frac{1}{2} m v^{2} cos^{2}[/tex] θ.

Given,

Mass of the projectile = m

The height at which projectile is given 'h'.

Speed of the projectile is 'v'.

As the projectile is fired horizontally, that is the angle θ = 0 degree.

And 'g' is the acceleration due to gravity.

(a) The work done when the applied force and distance or height (h) are in parallel:

W = Fh (cosθ) .....(1)

Where F is the force exerted by the gravity on the projectile

So, F can be written as, F = mg ....(2)

Putting equation (2) in (1).

We get, W = mgh (cosθ)

Where θ = 0 degree

So, W = mgh (cos[tex]0^{0}[/tex])

W = mgh

This is the work done by the gravity on the projectile when the projectile is in horizontal direction.

(b) To determine kinetic energy of the projectile in horizontal:

Velocity component at x axis will be [tex]v_{x}[/tex] =  v cos θ

In general the Kinetic energy of an object moving with mass (m) with a velocity 'v' = [tex]\frac{1}{2}[/tex]m[tex]v^{2}[/tex]

For a projectile it can be written as, K.E = [tex]\frac{1}{2}[/tex] m(v cos θ)^2

Or, K.E = [tex]\frac{1}{2} m v^{2} cos^{2}[/tex]θ

Hence, the work done by the projectile is 'mgh' and its kinetic energy will be  [tex]\frac{1}{2} m v^{2} cos^{2}[/tex] θ.

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The maximum difference in potential energy would be [tex]ΔE max​ =8.12×10 −4 eV[/tex]

The energy that is held in an object as a result of its position in relation to a zero position is known as potential energy, to put it simply. If an object is placed at a height above (or below) the zero height, it has gravitational potential energy.

Energy that is conserved or stored in a substance or object is known as potential energy. The position, organization, or state of the object or substance determines the amount of stored energy.

It can be pictured as energy with the "potential" to perform labor. The energy will be released when the object's position, configuration, or state changes.

For instance, compressing a spring costs energy. However, what happens to that energy once the spring has been compressed? After all, we are aware that energy can only be changed from one form to another; it cannot be generated or destroyed.

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The average intensity of an electromagnetic wave with a peak magnetic field strength of B is I = cB^2/2µo

Define the intensity of an EM wave?

The energy that crosses per second per unit area perpendicular to the electromagnetic wave's direction is what is referred to as the wave's intensity.

Any wave's energy is proportional to its amplitude squared. Thus, the intensity of electromagnetic waves can be written as

I = cε0E^2/2

where

I represents the average intensity of the EM wave in W/m^2.

E represents the strongest possible electric field created by a continuous sinusoidal wave

c  is the speed of light

ε0 is the permitivitty of free space

If B is the strongest possible magnetic field and µo  is the permeability of free space, then the average intensity of an electromagnetic wave, I, can also be represented in terms of the strength of the magnetic field using the relationships

B = E/c, and

ε0 = 1/µo c^2

The highest magnetic field strength B can also be used to express this as,

I = cB^2/2µo

Hence, the average intensity of an electromagnetic wave with a peak magnetic field strength of B is I = cB^2/2µo

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After an object has travelled a certain distance, the student must calculate the work that is done on it when an external force is applied to it.

An object at location x = 0 experiences an external force F from a string as it traverses a distance D over a horizontal surface for a period of time . As the thing moves, the force changes so that it becomes less.

The final kinetic energy of the object must have been lower than the work performed on it by the applied force, indicating that another external force must have been involved.

Therefore, the learner must determine the work that is done on an object when an external force is applied after it has moved a particular distance.

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Due to this shift in day length, 0.409 seconds were added. Ocean's atmosphere and depth increased by about 31.2 m as a result of the melting of the polar ice caps and the subsequent return of water.

The oblique angle at which the sun's energy enters the Earth's atmosphere causes it to spread out over a larger area, be less concentrated, and travel a greater distance through the atmosphere before it can be absorbed during , resulting in less intense solar radiation in the polar ice regions than in other parts of the planet. Are known as polar ice.

According to the available information, the oceans were about 15.1 metres (m) deeper, which actually means that the water level rose by 15.1 meters.

As a result, the following formula will be used to calculate the change in the earth's radius: dR=15.6 m

dT = 2TdR/R = 2*24*3600*15.1/6371000 = 0.409s

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802.11 ac  can transmit data at 1300 mbps (megabits per second) or 162.5 mbps (megabytes per second).

You may have noted that the time between 802.11n and 802.11ac was six years. In terms of technology, this is an aeon, and the main advantage that 802.11ac has benefited from is speed.

WiFi is frequently advertised at "theoretical" rates; according to this standard, 802.11ac can do 1300 Mbps, which is the equivalent of 162.5 MB/s (MBps). This is three times quicker than the normal 802.11n speed of 450Mbps.

These speeds are the issue. The fastest 802.11ac real world speeds reported in testing are roughly 720Mbps. In the real world, no one ever achieves theoretical speeds (90MBps). While 802.11n has a peak speed of roughly 240Mbps (30MBps), the 3x estimate is still accurate.

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Necessities are inelastic.

Goods that are taken into consideration important have a low elasticity of call for. Strength, fuel, oil, and water are all particularly inelastic because clients depend upon these as requirements in place of luxuries.

An elastic call is one wherein the exchange in the amount demanded because of a change in rate is big. An inelastic call is one in which the alternate quantity demanded because of a change in price is small.

Perfectly inelastic merchandise would be something like air or water, and no person can sincerely restrict that at this factor in time.

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The definition of amplitude is that displacement of the particle from the main position is known as the amplitude.

Suppose that there is a spring which has a block connected to one of its end and the other and is connected to a solid rigid wall.

Now let us say that we give a push to the block.

If ignore the air resistance, then we will observe that, the block will show a to and from movement from the initial position of the spring which is in the middle of the to extreme positions of the spring.

The distance that is covered by the block when it most away or towards the spring is known as the amplitude of the spring block system.

This is how we conclude that the displacement of the particle about its mean position is known as amplitude.

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It would take a human little more than 22 years to cross the same distance if they could move at half the speed of light.

The speed of light is 300,000 kilometres (186,000 mi) per second. In other words, light covers the same distance in a single second as it would take you to circle the Earth 7.5 times! About one light second separates you from the moon.

Even time is a relative concept. This led scientists to conclude that the speed of light is constant and unaffected by the observer.

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Solar thermal and photovoltaic (PV) are two different technologies used to harness energy from the sun. Solar thermal systems use the sun’s rays to heat water or air while PV systems convert sunlight directly into electricity.

Both technologies have similarities and differences, and each can be used in various applications. The most important similarity between solar thermal and photovoltaic systems is that they both use the sun’s energy to produce energy. In both cases, the sun’s rays are converted into usable energy. Solar thermal systems use the sun’s heat to heat water or air, while PV systems use the sun’s light to generate electricity. Both systems are also relatively easy to install and maintain, and require little to no additional energy input.

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A solid body rotating about an axis has rotational kinetic energy that is proportional to both its moment of inertia and its angular speed of rotation about the axis.

The formula is: K=(1/2)I[tex]w^{2}[/tex]

The most straightforward form of rotational motion is a circle rotating around an axis. The rotational kinematics equations then resemble the linear kinematics equation:

θ [tex]= w_{i} t + \frac{1}{2} \alpha t^{2}[/tex]

[tex]w_{f} = w_{i} + \alpha t[/tex]

where α is the angular acceleration,

ω is the angular speed,

θ is the angle traveled and

t is the time.

Given data:

Mass of the disk, [tex]m_{d}[/tex]=3.3 kg

The radius of the disk, R=0.26m

Mass of the rod, [tex]m_{r}[/tex]=1.2 kg

Length of the rod, L=0.72 m

a) Think about the equation used to calculate the rod's moment of inertia.

[tex]I_{rod}[/tex] = [tex]\frac{1}{3} m_{r} L^{2}[/tex]

Calculate the moment of inertia of each rod about the axis of rotation.

[tex]I_{rod}[/tex] = [tex]13 * (1.2) * (0.72)^{2}[/tex]

[tex]I_{rod}[/tex] = [tex]0.207 kg m^{2}[/tex]

b) A disk's moment of inertia around an axis that passes through its center and is perpendicular to the disk is:

[tex]I_{disk}[/tex] = [tex]\frac{1}{2} m_{d} R^{2}[/tex]

We have,

[tex]I_{disk}[/tex] = [tex]\frac{1}{2} (3.3) (0.26)^{2}[/tex]

[tex]I_{disk}[/tex] = [tex]0.112 kg m^{2}[/tex]

c) The entire ceiling fan's moment of inertia.

[tex]I_{fan} = 5 I_{rod} + I_{disk}[/tex]

[tex]I_{fan} = 5 (0.207) + 0.112\\I_{fan} = 1.147 kg m^{2}[/tex]

d) Here we are given the angle covered and the time for it.

We can find the angular acceleration from the formula:

θ = [tex]\frac{1}{2} \alpha t^{2}[/tex]

We have:

θ = 13 rev

θ = 13(2π) rad

θ = 26π rad ≈ 81.68 rad

Therefore we have:

[tex]\alpha = 2[/tex]θ / [tex]t^{2}[/tex] = [tex]\frac{2(26\pi )}{3.1^{2} }[/tex] = 17 rad / [tex]s^{2}[/tex]

e) To find the final angular velocity of the fan we have:

[tex]w_{f} = w_{i} + \alpha t[/tex]

Substitute [tex]w_{i}[/tex] = 0, [tex]\alpha[/tex] = 17 rad / [tex]s^{2}[/tex], and t=3.1s in the above expression:

[tex]w_{f} = 0 + 17 (3.1)[/tex]

[tex]w_{f} = 52.7 rad / s[/tex]

f) Consider the formula used to calculate the final rotational kinetic energy of the fan.

K = [tex]\frac{1}{2} I_{fan} w_{f}^{2}[/tex]

Substitute the values.

K = [tex]\frac{1}{2} (1.147) (52.7)^{2}[/tex]

K = 1593 J

g) The spinning energy of the fan decreases by half when it is adjusted to a lower speed.

This can give us angular speed.

[tex]K_{f} = \frac{K}{2}[/tex]

[tex]K_{f} = \frac{1593}{2}[/tex]

[tex]K_{f} = 796.5 J[/tex]

Calculate the final angular speed of the fan.

[tex]K_{f} = \frac{1}{2} I_{fan} w_{f}^{2}[/tex]

[tex]w_{f} = \sqrt{\frac{2K_{f}}{I_{fan} } }[/tex]

Substitute the values.

[tex]w_{f} = \sqrt{\frac{2(796.5)}{1.147} }[/tex]

[tex]w_{f} = 37.3 rad / s[/tex]

h) The angular acceleration is calculated when the fan slows down by

[tex]w_{f} = w_{i} + \alpha t[/tex]

[tex]\alpha[/tex] = [tex]\frac{w_{f} - w_{i} }{t}[/tex] = [tex]\frac{37.3 - 52.7}{3.1}[/tex] = − 4.97 rad / [tex]s^{2}[/tex]

Therefore, the magnitude of the angular acceleration is:

|[tex]\alpha[/tex]| = 4.97 rad / [tex]s^{2}[/tex]

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The capacitance of the plate is 2.2125 × [tex]10^-^1^2[/tex] F

Given : dimensions of the plate = 1 cm x 1 cm = [tex]10^-^2[/tex] m ×  [tex]10^-^2[/tex] m

The given separation is 0.4mm

to convert this dimension into m

we get

separation or d = 4 × [tex]10^-^4[/tex] m

let capacitance be represented by c

Formula of capacitance = [tex]\frac{AE_{0} }{d}[/tex]

here A = = [tex]10^-^2[/tex] m ×  [tex]10^-^2[/tex] m  = [tex]10^-^4[/tex] m²

And E₀ = 8.85 × 10^-12 F

and d =  4 × [tex]10^-^4[/tex] m

On substituting these values in the formula we get

C = [tex]10^-^4[/tex] ×  8.85 × 10^-12/ 4 × [tex]10^-^4[/tex]

C = 2.2125 × [tex]10^-^1^2[/tex] F

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The angle of incidence at the first mirror will this ray strike the midpoint of the second mirror is 34.6°

Two plane mirrors intersect at right angles. A laser beam strikes the first of them at a point d = 10.0cm from their point of intersection.

To strike the midpoint of the second mirror, the ray of light will have to travel half of the distance vertically

i.e. 29/2 = 14.5

We can solve this through trigonometry.

Let the angle between the ray and the vertical plane mirror is known as α

tan α = 10/14.5

α =  = 34.6°

The angle of incidence is the angle between the ray and the normal line of the mirror.

Let the angle of incidence of the first mirror be β

β = α = 34.6

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The pressure tends to zero pascals when the gas volume approaches very high volumes. On the other end of the graph, we can observe that the pressure tends to infinity as the volume decreases towards zero.

Volume and pressure are inversely related. Therefore, the volume will decrease as the pressure does, and vice versa.

Now, as the volume gets closer to zero, the pressure will dramatically rise and eventually tend to infinity. At v=0, the pressure-volume curve will asymptote.

As a result, when the volume comes to zero, the pressure will tend to infinite.

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A scientific model's primary goal is to depict empirical things, physical processes, and events in an objective and logical manner, something that is challenging to perceive or comprehend.

Models can aid scientists in explaining their concepts. In many scientific contexts, models are of utmost significance.

Scientists use models to inexpensively and practically duplicate situations or theories. These models assist researchers, gather data to forecast outcomes, test hypotheses, and communicate scientific concepts to non-specialists. As new data is uncovered, scientists frequently update and modify their models. Models are visual aids that assist scientists in communicating complex material when used for presenting ideas or results.

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Answer:

[tex]d=4\frac{g}{cm^3}[/tex]

Explanation:

[tex]d=\frac{m}{v}\\m=20g\\v=5cm^3\\d=\frac{20g}{5cm^3}\\d=4\frac{g}{cm^3}[/tex]

The change in the velocity of the baseball is 2 m/s.

Given that,

Mass of the baseball, m = 0.5 kg

Force, F = 10 N

Time duration of force, t = 0.1 s

To find, The change in velocity of the baseball.

Solution,

The impulse imparted by an object is given by :

Impulse is equal to the change in momentum of an object i.e.

(v-u) is the change in velocity of the baseball

(v-u)= 2 m/s

So, the change in velocity of the baseball is 2 m/s.

The pace is the directional speed of an item in movement as an indication of its price of change in role as located from a specific frame of reference and as measured by a specific general of the time.

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The true statement is the Destroyer would have some component of its velocity in the southern direction.

Relative terminology that compare the position of one item to another can be used to express direction, such as up, down, in, out, left, right, forward, backward, or sideways. The four cardinal directions, north, south, east, and west, can also be used to represent direction. the line that something lies, faces, moves, etc. with reference to the place or region toward which it is directed: the act or instance of directing Northward movement was made by the storm. the actual region or point: The north is the direction. The velocity vector's direction of orientation indicates the motion's direction. To apply your example of a bullet thrown straight up, the velocity vector will seem as follows because only its height, z, is changing: v= (0,0,dzdt).

To find the direction of the vector v = (x, y), use the formula = arctan(y/x), where is the lowest angle the vector makes with the horizontal axis and x and y are its two constituents.

The direction of magnetic field lines surrounding a current-carrying conductor can be found using Maxwell's Right-Hand Thumb Rule. It says that if the thumb of the right hand represents the direction of current flow, the remaining curled fingers determine the direction of the magnetic field around it.

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The internal resistance of the car battery is 0.0395 Ω. The result is obtained by using the formula to find the electromotive of Volts.

Electromotive of Volts can be counted by the following formula.

ξ = V + Ir

or

ξ = IR + Ir

Where

We have:

What is the internal resistance? (r = ?)

By using the above formula, we get

ξ = V + Ir

Ir = ξ - V

r = (ξ - V)/I

The internal resistance is

r = (9.0 - 12.0)/76

r =  0.0395 Ω

Hence, the internal resistance of car battery is 0.0395 Ω.

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Yes this statement is true about electrical resistance circuit.

What is electrical resistance?

electrical resistance is a force that counteracts the flow of current.

Sol- when two lamps are connected in parallel to a battery, the total electrical resistance that the battery senses is more than the resistance of either . Beacuse In a parallel circuit each bulb is in its own circuit. As bulbs are added the resistance in the circuit decreases since each circuit is another pathway for electrons to move from one end of the circuit to the other.when two lamps are connected in series to a all the  battery the electricals resistance that the battery's senses is the more than the resistence of either lamp.

As each bulb is connected in parallel to the battery, each has the same potential difference across it as the all of  voltage across the battery of the  terminals. All other to the potential differences are zero, as all the wires have to the zero resistance.

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The gravitational field produced by the Sun, Earth, Moon, and other planets extends throughout space. However, the gravitational pull of that distance diminishes.

What is gravitational pull?
The attraction that the earth has on something or that something has on the earth is known as the gravitational pull of a earth. It can be calculated using the object's mass, Earth's mass, the separation between the object's and Earth's centres, and the universal gravitational continuous, a proportionality constant that has been precisely measured. It is 6.674 x 10-11 in size. The weight of an item on the earth's surface is one of the most typical illustrations of this pull.

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These grasshopper-related insects generate massive swarms that travel across areas. Since the Pharaohs ruled ancient Egypt, plagues of locusts have destroyed societies and continue to cause devastation now.

Invertebrates (animals without a backbone) have a hard exterior covering called an exoskeleton. The head, thorax, and abdomen make up an insect's three-part body. The majority of mature insects also have wings, and they all have six legs. Insects come in more than a million different varieties.

Ants are the most common bug in the world, which should not be surprising. There are around 10,000 species of these colonial hymenopterans, with an estimated population size of 10–100 trillion individuals worldwide.

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For this given case of inelastic collision, statement C is true that is, vf is greater than v2, but less than v1.

According to the conservation of linear momentum, when two or more bodies interact, their combined momentum stays constant. So, the total momentum of the system just prior to the collision and the total momentum immediately following the collision are the same in a system of colliding bodies.

The collision is considered to be perfectly inelastic if the two bodies stick together after colliding and move at the same speed. Inelastic collisions are collisions where the kinetic energy is not preserved.

Thus, the velocity of both the bodies together (vf) is greater than v2, but less than v1.

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The complete question is:

The two particles are both moving to the right. Particle 1 catches up with particle 2 and collides with it. The particles stick together and continue on with velocity vf. Which of these statements is true?

a. vf= v2

b. vf is less than v2.

c. vf is greater than v2, but less than v1.

d. vf= v1

The discussion of light and the expansion of Universe are the dark energy and dark matter exist.

A dark matter is a theoretical astronomical thing postulated by the scientist which is believe to take several forms and it is non luminous nature which exist in far space.

Similarly dark energy is the energy that is postulated by the scientist which is believe to be a force that is working against the gravity that almost all the universe and is constantly causing the expansion of the space.

Scientist in studied the nature of light and how the light disorted in the Galaxy clusters computer to a road map that dark matter exist in the universe. The constant expansion of the universe is itself a proof of presence of the dark energy.

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The change in total kinetic energy of the system that occurs during the collision is 0.05 J.

Given that, m₁ = 0.200 kg

m₂ = 0.400 kg

u₁ = ?

u₂ = 0

v₁ = 0.120 m/s

v₂ = 0.650 m/s

According to the law of collision, we have

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

Substituting the given data in the above equation, we have

m₁ u₁ = m₁ v₁ + m₂ v₂ - m₂ u₂

m₁ u₁ = 0.2* (-0.12) + 0.4* 0.65 - 0.4* 0

0.2* u₁ = -0.024 + 0.26

u₁ = 1.18 m/s

Change in kinetic energy = Kinetic energy before collision - Kinetic energy after collision

= -1/2 (0.2) 0.12² - 1/2 (0.4) 0.65² + 1/2 (0.2) 1.18² = -0.00144 - 0.0845 + 0.1392 = 0.05326 J

Thus, the change in kinetic energy is 0.05 J.

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A represents the so-called sublimation of state. represents the evaporation, a state change. C stands for melting, a change of state.

A liquid turns into a gas through evaporation. Water vapor is created when liquid water evaporation turns it into a gas. Water is helped to evaporate and return to the atmosphere by the heat of the sun. There, it creates a cloud and returns to being water in the form of vapor.

Evaporation is the process by which liquid water transforms into gaseous water (water vapor). Water from the Earth's surface is carried into the atmosphere by evaporation. Evaporation occurs when heat energy causes the bonds holding the water molecules together to fall apart.

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The vibrating energy carried from one to another via sound waves. The atoms in the tuning fork vibrate and transfer from one place to another. As a result, the situation is equivalent to analogous effect for light.

Light generated by resonant vibrations of an electron orbiting one atom can be absorbed by an electron in another atom with the same resonant frequency of vibration. In reality, visible "light" is a type of radiation, which is defined as energy that moves in the form of electromagnetic waves. It can alternatively be defined as a continuous flow of particle-like 'wave-packets,' known as photons, that travel at the speed of light (about 300 000 kilometres per second). Light waves emanate from a source. Each wave is composed of two parts: an electric and a magnetic component. That is why light is referred to be Electromagnetic Radiation.

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Your authority will be weakened by improper grammar and mechanics. Keep an eye out for recurring grammatical mistakes or other technical errors in your writing, and attempt to fix them by getting feedback.

The term "mechanics" relates to linguistic conventions including capitalization, punctuation, and spelling. To effectively explain your ideas in a paper, you need to be aware of both language and mechanics. Your intended message may be accidentally changed by grammatical mistakes in your writing. Your essay or advertisement's meaning might be altered by a single, recurring grammatical mistake or misspelled word. It speaks of the components of speech and how they work together to generate sentences. Use coordinating conjunctions and punctuation to prevent run-on sentences and comma splices. Mechanics are the laws of written language, such as capitalization, punctuation, and spelling. To prevent sentence fragments, use punctuation and coordinating conjunctions.

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When submerged in a liquid, objects with a lower density will float. For instance, because the egg has become less dense than salt water, it floats in the latter.

Liquids lack set shapes but do have defined volumes. Blood, oil, and water are a few examples of liquids. A state of matter known as a liquid has a defined volume but no set shape. Alternatively said, a liquid adopts the shape of its container.

The volume retention and conformity to the shape of the container of such a liquid are two of its most visible physical characteristics. When liquid is poured it in to a container, the container's shape is assumed, and as long as the liquid state is maintained, the substance will stay inside the container.

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Furthermore, as the spring is pushed down, the work done is stored as elastic potential energy. As a result, the total of elastic potential energy and gravitational potential energy will rise.

If an item is above (or below) the zero height, it has gravitational potential energy. If an item is at a position different than the equilibrium position on an elastic medium, it has elastic potential energy.

Gravitational potential energy is energy contained in a vertically held item. Elastic potential energy is stored energy in things that can be stretched or squeezed.

The amount of the force necessary to modify the length of a spring-like item.

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