A pendulum has a bob with a mass of 25.0kg and a length of 0.750m. It is pulled back a distance of 0.250m. What is the period of the pendulum?

The flywheel will not come to rest as the given frictional torque of 4.0 N·m is not enough to stop it from rotating.

The rate of change of angular momentum (L) of the flywheel is equal to the net torque (τ) acting on it. Mathematically,

τ = dL/dt

Since the flywheel is initially rotating with an angular velocity of 400 rad/s, its angular momentum is given by:

L = Iω

where I is the moment of inertia of the flywheel and ω is its angular velocity. The moment of inertia of a solid disk is given by (1/2)MR², where M is the mass of the disk and R is its radius. Therefore, the moment of inertia of the flywheel is:

I = (1/2)MR²

Substituting the given values, we get:

I = (1/2)(1.0 x [tex]10^6[/tex])/(π(0.2)²) = 79577.47 kg·m²

So, the angular momentum of the flywheel is:

L = Iω = 79577.47 x 400 = 31,831,888 kg·m²/s

The frictional torque acting on the flywheel is 4.0 N·m, so we have:

τ = 4.0 N·m

Setting these two equations equal to each other, we get:

dL/dt = τ

d(Iω)/dt = 4.0

I(dω/dt) + ω(dI/dt) = 4.0

Since the moment of inertia of the flywheel is constant, dI/dt = 0. So we have:

I(dω/dt) = 4.0

Substituting the values of I and τ, we get:

79577.47 x (dω/dt) = 4.0

dω/dt = 5.03 x [tex]10^-^5[/tex] rad/s²

The flywheel will come to rest when its angular velocity becomes zero. Using the equation of motion for rotational motion:

ω = ω0 + αt

where ω0 is the initial angular velocity, α is the angular acceleration, and t is time.

Substituting the values of ω, ω0, and α, we get:

0 = 400 + (5.03 x [tex]10^-^5[/tex])t

t = -400/(5.03 x [tex]10^-^5[/tex])

t = -7.96 x [tex]10^6[/tex] s

Since time cannot be negative, the flywheel cannot come to rest in this case. This means that the frictional torque of 4.0 N·m is not enough to stop the flywheel from rotating.

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It is difficult to predict the exact path the ping pong ball will follow.

The path the ping pong ball will follow when it leaves the track depends on its velocity and direction of motion. If the ball has enough velocity and momentum, it will continue moving in a straight line tangent to the point where it left the track. If the ball has insufficient velocity and momentum, it will fall due to gravity and follow a parabolic path downwards. The curvature of the circular track may also cause the ball to curve in a particular direction, depending on the direction of its initial motion and the angle at which it exits the track. However, without additional information about the specifics of the situation, it is difficult to predict the exact path the ping pong ball will follow.

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The phase difference when two waves, traveling in the same medium, undergo constructive interference.

When two waves traveling in the same medium interfere constructively, their amplitudes add up to produce a wave with a larger amplitude than either of the individual waves. The phase difference between the two waves in this case is zero degrees or a multiple of 360 degrees.

To explain this, consider two waves of the same frequency and amplitude, traveling in the same direction in a medium. When they overlap, their amplitudes at each point add up. If the two waves are in phase, meaning their peaks and troughs align perfectly, the amplitude of the resulting wave is the sum of the individual amplitudes.

However, if the two waves are out of phase, meaning their peaks and troughs do not align perfectly, the amplitude of the resulting wave is smaller than the sum of the individual amplitudes. The degree of out-of-phase is given by the phase difference between the two waves.

In constructive interference, the phase difference between the two waves is zero or a multiple of 360 degrees, resulting in the peaks and troughs aligning perfectly and the amplitude of the resulting wave being larger than the amplitude of either of the individual waves.

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This reaction is an example of gamma emission as the gamma rays are emitted during the formation of the stable nucleus from the unstable one. Thus, option C is correct.

When the unstable or parent nucleus undergoes decaying, it forms a stable nucleus without any change in mass and atomic number, but the release of high energy waves called Gamma rays is called Gamma decay or Gamma emission.

Hence, the ideal solution is C) Gamma emission.

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As a result, passive responses are limited to short distances and cannot propagate long distances like action potentials. The given statement is True.

Passive (subthreshold) responses are graded potentials that decay rapidly with distance. These responses occur when a neuron receives small, subthreshold signals from other neurons. They do not reach the threshold for firing an action potential, and therefore do not propagate along the axon. Instead, the signal decays with distance from the site of stimulation, due to the passive leakage of charge across the neuronal membrane. This decay is caused by the resistance of the membrane and the leakiness of the ion channels that make up the membrane. As a result, passive responses are limited to short distances and cannot propagate long distances like action potentials.

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False. Whenever there is a change in direction, the velocity may change, but it will not necessarily be zero at the instant the direction changes.

Velocity is a vector quantity that takes into account both the speed and direction of an object's motion.

So, when there is a change in direction, the velocity will change as well. However, the magnitude of the velocity (i.e., the speed) may remain constant even as the direction changes.

Therefore, the statement is false. Whenever there is a change in direction, the velocity may change, but it will not necessarily be zero at the instant the direction changes.

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The resultant speed of the kick is 26.13 m/s horizontally.

The velocity of the soccer, v₁ = 7 m/s

Velocity with which the ball is kicked, v₂ = 30 m/s

Angle at which ball is kicked, θ = 10°

After kicking, the ball will follow a projectile motion.

The resultant speed of the kick,

v = √v₁² + (v₂² cos²10)

v = √49 + 633.6

v = 26.13 m/s

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Rippling the mass per unit length of a guitar string will result in no change to the wave speed in the string by  factor of 1.00 (i.e., no change).

This is so because the tension and linear density of the string, rather than the mass of the string, determine the wave speed. A string's tension must rise as its mass per unit length increases in order to keep the wave speed constant.

As a result, raising a guitar string's mass per unit length will not alter the wave speed of the string. The tension and linear density of a string affect both its wave speed and density.

The wave speed of a guitar string will not change in any way when the mass per unit length is tripled.

Complete Question:

Rippling the mass per unit length of a guitar string will result in changing the wave speed in the string by what factor?

a. 1.73

b. 1.00 (i.e., no change)

c. 3.00

d. 0.58

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As the base elevation of a thundercloud gets lower and lower, the possibility of lightning strike increases. Thunderstorms form when warm, moist air rises and cools, forming clouds.

These clouds are known as cumulonimbus clouds, which are tall and have a flat base. The base of a cumulonimbus cloud can vary in height, depending on the temperature and moisture content of the air below it.

The lower the base of a thundercloud, the closer it is to the ground, and the more likely it is to produce lightning strikes. This is because lightning is an electrical discharge that occurs when there is a difference in charge between two objects, such as the cloud and the ground. When the base of a thundercloud is low, it means that the cloud is closer to the ground, which increases the likelihood of a charge difference between the cloud and the ground.

Furthermore, the lower base of a thundercloud can also mean that there is more moisture in the air below it, which can lead to more lightning strikes. This is because moisture in the air can help to conduct electricity, making it easier for lightning to travel from the cloud to the ground.

In conclusion, the lower the base elevation of a thundercloud, the greater the possibility of lightning strike due to the increased proximity to the ground and higher moisture content. It is important to stay indoors and avoid outdoor activities during thunderstorms to avoid the risk of being struck by lightning.

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They can cause other types of artifacts in ultrasound imaging.

Enhancement artifact in ultrasound imaging is caused by unexpectedly low acoustic attenuation in the tissue being imaged.

Attenuation refers to the weakening of the ultrasound signal as it passes through tissue, and it is influenced by various factors such as the tissue's density, composition, and structure. When an area of tissue has lower attenuation than its surroundings, more of the ultrasound signal passes through that area, resulting in an increase in signal intensity and brightness on the image. This can give the false impression that the tissue has a higher density or composition than it actually does, leading to an enhancement artifact.

Therefore, the correct answer is c. unexpectedly low acoustic attenuation.

Sound beams bending, linear array transducer architecture, and acoustic energy radiating in a direction other than the beam's main axis are not direct causes of enhancement artifacts. However, they can cause other types of artifacts in ultrasound imaging.

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The correct answer about luminosity of the star is c. there is insufficient information to answer this question.

The luminosity of the star is dependent on the surface temperature and it's size. It implies that the stars with same size and higher temperature will have higher luminosity due to higher emission of energy per unit surface area.

Similarly, at the same temperature, the star of bigger size will be more luminous. Now the question states both the variables without exact information for comparison making it difficult to determine.

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The horizontal force on the green block is greater than the vertical force on red block. F₂ > F₁.

According to Newton's third law of motion, every action is followed by a corresponding, countervailing reaction. Two separate bodies are affected by these forces of activity and response.

From the figure, it is clear that the force F₂ is acting such that, the whole system is being pulled.

F₂ = (m₁ + m₂)a

Also,

F₁ = m₁g

So,

m₁ = F₁/g

Therefore, the horizontal force can be given as,

F₂ = (F₁/g + m₂)a

Thus, we can say that horizontal force on the green block is greater than the vertical force on red block.

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Satellite B has 0.5 times the speed of A meaning Satellite B has half the speed of Satellite A.

To compare the speed of Satellite B to Satellite A, we will use the formula for the orbital speed of a satellite, which is:

v = √(GM/R)

where v is the orbital speed, G is the gravitational constant, M is the mass of the planet, and R is the orbital radius.

Let v_A be the orbital speed of Satellite A and v_B be the orbital speed of Satellite B. We know that the orbital radius of Satellite B (R_B) is four times that of Satellite A (R_A). Therefore, R_B = 4R_A.

Now, we can write the equations for both satellites:

v_A = √(GM/R_A)
v_B = √(GM/R_B)

Since R_B = 4R_A, we can rewrite the equation for Satellite B:

v_B = √(GM/(4R_A))

Now, we can compare v_B and v_A:

v_B/v_A = [√(GM/(4R_A))]/[√(GM/R_A)]

By simplifying the equation, we get:

v_B/v_A = √(R_A/4R_A) = 1/2

So, Satellite B has half the speed of Satellite A. In other words, B has 0.5 times the speed of A.

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The magnitude of the object's velocity at the end of the 3.0-s interval is approximately 9.2 m/s. The correct answer is option 1) 9.2 m/s.

To find the magnitude of the object's velocity at the end of the 3.0-s interval, we need to first determine the acceleration and then the final velocity in both x and y directions.

1. Calculate acceleration:
a = F/m
a_x = 2.0 N / 2.0 kg = 1.0 m/s² (i direction)
a_y = 4.0 N / 2.0 kg = 2.0 m/s² (j direction)

2. Calculate final velocity in both directions:
v_x = u_x + a_x * t
v_x = 4.0 m/s + 1.0 m/s² * 3.0 s = 7.0 m/s (i direction)

v_y = u_y + a_y * t
v_y = 0 m/s + 2.0 m/s² * 3.0 s = 6.0 m/s (j direction)

3. Calculate the magnitude of the final velocity:
v = √(v_x² + v_y²) = √((7.0 m/s)² + (6.0 m/s)²) = √(49 + 36) = √85 ≈ 9.2 m/s

So, the magnitude of the object's velocity at the end of the 3.0-s interval is approximately 9.2 m/s. The correct answer is option 1) 9.2 m/s.

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In oxidative phosphorylation, cytochrome c acts as: A. a 1-electron carrier.

The oxidative phosphorylation is the one of the steps in cellular respiration. The cellular respiration involves glycolysis, Krebs cycle and final step of oxidative phosphorylation, which leads to generation of maximum amount of ATP compared to other steps.

The cytochrome c and other cytochromes, the heme containing proteins, transfer the electrons within the mitochondrial inner membrane space and matrix. Cytochrome c transfer one electron from complex III to complex IV.

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An Earth observer can only see half of the celestial sphere at one time. This half changes as the Earth rotates, allowing the observer to see different regions of the celestial sphere over the course of a night or a year.

An Earth observer can see only one-half of the celestial sphere at a time. Here's why:

Since the observer can only see objects above the horizon, the observer can only see the half of the celestial sphere that is currently above their local horizon.

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A force of approximately 6.28 x 10⁵ N is necessary to stretch a 2.0-mm-diameter steel wire (Y = 2.0 x 10¹¹ N/m²) by 1.0%.

To calculate the force necessary to stretch a 2.0-mm-diameter steel wire (Y = 2.0 x 10¹¹ N/m²) by 1.0%, follow these steps:

1. Calculate the cross-sectional area (A) of the wire using the formula A = πd²/4, where d is the diameter.
2. Calculate the strain (ε) using the percentage of elongation.
3. Use Hooke's Law to find the force (F) using the formula F = YAε, where Y is the Young's modulus.

Step 1: Calculate the cross-sectional area (A) of the wire.
A = (π x (0.002 m)²) / 4
A ≈ 3.14 x 10⁻⁶ m²

Step 2: Calculate the strain (ε).
ε = 1.0% = 0.01

Step 3: Use Hooke's Law to find the force (F).
F = YAε
F = (2.0 x 10¹¹ N/m²) x (3.14 x 10⁻⁶ m²) x 0.01
F ≈ 6.28 x 10⁵ N

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If the distance between two point charges is doubled while the size of the charges remains the same, the force between the charges is multiplied by 1/4 or 0.25.

The force between two point charges is determined by Coulomb's Law, which states that the electrostatic force (F) between two point charges (q1 and q2) is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance (r) between them.

Mathematically, Coulomb's Law is expressed as:

F = k * (q1 * q2) / [tex]r^2[/tex]

Where k is the electrostatic constant (approximately 8.99 × [tex]10^9 N m^2 C^{-2})[/tex].

Now, let's consider the scenario in which the distance between the charges is doubled. This means the new distance between the charges will be 2r. According to Coulomb's Law, the new force (F') between the charges can be calculated as follows:

F' = k * (q1 * q2) / [tex](2r)^2[/tex]

When we simplify this expression, we get:

F' = k * (q1 * q2) / (4 * [tex]r^2[/tex])

Now, if we compare this new force (F') with the original force (F), we can see that:

F' = F / 4

This indicates that when the distance between two point charges is doubled while the size of the charges remains the same, the force between the charges is multiplied by 1/4 or 0.25. Therefore, the force between the charges is reduced to one-fourth of its original value when the distance is doubled.

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Since the relationship between wavelength and frequency is inverse, the wavelength of the sound coming from source A is half that of the sound coming from source B. This implies that wavelength is cut in half as frequency is doubled.

The distance between adjacent, identical wave components, such as between adjacent compressions as shown in Figure 17.8, is the wavelength of a sound. The frequency is the number of waves passing a point in a unit of time, and it is the same as the frequency of the source.

When anything vibrates, a sound is made. The medium (such as water, air, etc.) around the vibrating body also vibrates. Air vibrations are referred to as longitudinal waves.

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A really low mass red dwarf can live as long as 100 billion years.

Hence, the correct option is C.

Red dwarfs are the most common type of star in the universe and are smaller and cooler than the Sun. Their mass can range from 0.08 to 0.5 solar masses. The less massive a red dwarf is, the longer it can live because it burns its fuel more slowly.

Red dwarfs generate energy through nuclear fusion, which involves converting hydrogen into helium. The rate of fusion depends on the mass of the star, with less massive stars fusing hydrogen at a slower rate. This means that low mass red dwarfs can burn their fuel for a much longer time than higher mass stars.

Theoretical models predict that red dwarfs with a mass of 0.08 solar masses can have lifetimes of up to 10 trillion years. However, these models are subject to uncertainties and depend on various factors, such as the star's metallicity, rotation rate, and magnetic activity.

In general, low mass red dwarfs are known for their longevity, with some potentially living for much longer than the current age of the universe. This means that they can be important targets for searches for potentially habitable planets around other stars.

Therefore, A really low mass red dwarf can live as long as 100 billion years.

Hence, the correct option is C.

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The strength of the magnetic field is 1.28 T.

Step 1: Calculate the mass per unit length of the wire:

m/L = 9.7 g / 0.05 m = 194 g/m

Step 2: Calculate the tension in each spring before the magnetic field is turned on:

F = k * x

where k is the spring constant and x is the displacement from the equilibrium position.

F = 2 * k * 0.0045 m = 0.009 kN

Step 3: Calculate the current in the circuit before the magnetic field is turned on:

I = V / R

where V is the voltage across the circuit and R is the total resistance.

I = 0.009 kN / 14 Ω = 0.00064 A

Step 4: Calculate the magnetic force on the wire:

Fm = BIL

where B is the strength of the magnetic field, I is the current in the wire, and L is the length of the wire.

[tex]Fm = B * 0.00064 A * 0.05 m = 3.2 * 10^-5 B N[/tex]

Step 5: Calculate the additional tension in each spring when the magnetic field is turned on:

[tex]F' = k * (0.0045 m + 0.0030 m) = 0.012 kN[/tex]

Step 6: Equate the magnetic force with the increase in tension:

[tex]Fm = 2 * (F' - F)3.2 * 10^-5 B N = 2 * (0.012 kN - 0.009 kN)B = 1.28 T.[/tex]

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The frequency of the vibrations caused by the tire's tread pattern when the car moves at 18.5 m/s is 925 Hz.

To find the frequency of the vibrations caused by the tire's tread pattern, we need to use the given information: the crevice spacing (2.00 cm) and the car's speed (18.5 m/s).

Step 1: Convert the crevice spacing from cm to meters.
1 cm = 0.01 m, so 2.00 cm = 2.00 * 0.01 m = 0.02 m.

Step 2: Calculate the number of crevices the tire passes per second (crevices per meter multiplied by meters per second).
Number of crevices per meter = 1 / 0.02 = 50 crevices/meter.
Number of crevices per second = 50 crevices/meter * 18.5 meters/second = 925 crevices/second.

Step 3: The frequency of the vibrations is equal to the number of crevices passed per second.
Frequency = 925 Hz.

So, the frequency of the vibrations caused by the tire's tread pattern when the car moves at 18.5 m/s is 925 Hz.

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A turbine takes in 1000-K steam and exhausts the steam at a temperature of 500 K. then its maximum theoretical efficiency of this system is

A heat engine is a system which converts heat into useful work. Carnot engine is an ideal engine which has maximum efficiency than any other engines. Carnot has showed that "no engine can be more efficient than Carnot engine and the 100% efficient engine can not be existed". It takes heat from the reservoir to do some work and it discharges some amount of heat to the sink. Reservoir is know as hot body and sink is know as cold body. Efficiency of the heat engine is given by,

Efficiency, η = output energy /input energy

Efficiency is nothing but to measure how much is the efficient  an engine or a device is.

in this problem,

1000 K steam is given to the turbine and it is getting  500 K steam at exhaust. it means that 500K of steam out of 1000K  is responsible for useful work.

hence efficiency = 500/1000 ×100 %=  50 %

hence the theoretical efficiency of this system 50%.

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If a pure gaseous element is subjected to an electrical discharge, the gas will glow because the electrical discharge causes the gas to become excited and emit radiation.

The resultant emission spectrum will be unique to the specific element, allowing scientists to identify which element is present. This phenomenon is known as spectroscopy, and it is used in various fields of science to study the composition and properties of materials. When a pure gaseous element (hot sample of gas) is subjected to an electrical discharge, the gas will glow and emit radiation. This phenomenon occurs because the electrical discharge excites the gas molecules, causing them to release energy in the form of light when they return to their lower energy states. The resultant glow and emitted radiation are characteristic of the specific element and can be analyzed using techniques like spectroscopy to identify the element's unique properties.

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The correct statement about motion of object is b. there is no rotational acceleration.

When an object is in rotational equilibrium, it means that the sum of all torques acting on the object is zero, resulting in no rotational acceleration.

However, the object may still be rotating at a constant angular velocity.

So, statement a. there are no torques acting on the object is not necessarily true, and statement c. the object is not moving and statement d. the object must be rotating are both incorrect.

Therefore, the correct one is b. there is no rotational acceleration.

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As a magnet is pushed toward a solenoid the strength of the B field passing through the loops of the solenoid will Increase.

A solenoid is an electrical device which consists of a coil of wire wrapped around a core and is used to convert electrical energy into a linear mechanical force. It acts as a switch in order to control the flow of electricity and is commonly used in a variety of applications, such as door locks, fuel injectors, and relay boards. Solenoids are often used for linear motion, such as in industrial machinery, robotic arms, and linear actuators. They are also used to control valves and pumps in hydraulic systems. Solenoids are made from a variety of materials, such as iron, copper, and aluminum, and their design can vary based on the application.

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a) The center of mass (CM) motion will also be tangential, in the same direction as the force.

b) The center of mass (CM) is moving at a speed of 4.24 m/s.

c) The disk is spinning at a speed of 4.99 radians per second.

d) The string has unwrapped from around the rim about 5.05 meters.

(a) The direction of the center of mass (CM) motion can be found using the direction of the applied force. Since the force is applied tangentially to the rim of the disk, the CM motion will also be tangential, in the same direction as the force.

(b) The work-energy principle can be used to find the speed of the CM:

W = ΔK + ΔU

where:

W = work done by the force

ΔK = change in kinetic energy of the disk

ΔU = change in potential energy of the disk

Since the surface is frictionless, there is no work done by friction. The only work done is by the applied force, which causes both translational and rotational motion. Therefore, the work done is:

W = Fd = 35.0 N * 5.2 m = 182 J

The change in kinetic energy can be split into translational and rotational components:

ΔK = (1/2)mv^2 + (1/2)Iω^2

where:

m = mass of the disk

v = speed of the CM

I = moment of inertia of the disk

ω = angular speed of the disk

The moment of inertia of a solid disk about its axis of rotation is (1/2)mr^2, so we can substitute this value:

ΔK = (1/2)mv^2 + (1/4)mv^2 = (3/4)mv^2

The change in potential energy is zero since the disk is not raised or lowered.

Substituting the given values and solving for v, we get:

182 J = (3/4) * 21.0 kg * v^2

v = 4.24 m/s (rounded to two decimal places)

Therefore, the CM is moving at a speed of 4.24 m/s.

(c) The angular speed of the disk can be found using the formula:

v = rω

where r is the radius of the disk. Substituting the given values and solving for ω, we get:

ω = v/r = 4.24 m/s / 0.85 m = 4.99 rad/s (rounded to two decimal places)

Therefore, the disk is spinning at a speed of 4.99 radians per second.

(d) The distance of string that has unwrapped from around the rim is equal to the distance traveled by the CM, which is given as 5.2 m. The circumference of the disk is 2πr, so the fraction of the circumference that has unwrapped is:

fraction unwrapped = distance traveled / circumference

= 5.2 m / (2π * 0.85 m)

= 0.966

Multiplying by the total length of string wrapped around the rim, which is equal to the circumference, we get:

length of string unwrapped = fraction unwrapped * circumference

= 0.966 * 2π * 0.85 m

= 5.05 m (rounded to two decimal places)

Therefore, about 5.05 meters of string has unwrapped from around the rim.

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The fish appears to be swimming at a speed of 16.2 cm².

What is distance ?

Distance is an object's overall movement, regardless of direction. Distance refers to the length of an object's real route as a whole. The displacement of an object between two points is defined as the straight line distance (shortest distance), measured from one position to the other.

What is speed ?

The rate of a directionally changing object's location. The SI unit of speed is created by combining the fundamental units of length and time. Meters per second (m/s) is the unit of speed in the metric system.

The relation between the actual speed, apparent speed and the index of refraction is given as

Therefore, we need to solve for the actual velocity.

V actual = V apparent × n

V actual = 12× 1.35

V actual = 16.2 cm²

Therefore, the fish appears to be swimming at a speed of 16.2 cm².

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The given statement "while discharging, the terminal voltage of the battery can never be greater than EMF of the battery" is true. Because, of internal resistance and other losses within the battery.

While discharging, the terminal voltage of a battery, which is the voltage across the battery's terminals when it is connected to a load, will always be less than the electromotive force (EMF) of the battery. The EMF of a battery represents the maximum potential difference that the battery can provide, and it is determined by the chemical reactions occurring within the battery.

During discharge, as the battery supplies energy to an external load, the chemical reactions inside the battery gradually deplete the stored energy, leading to a decrease in the voltage across the terminals. This is due to internal resistance and other losses within the battery. As a result, the terminal voltage of the battery will be lower than the EMF, and it will continue to decrease as the battery discharges.

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