The law of conservation of momentum states that the total momentum of an isolated system.

The rod's center of mass is measured from the left end of the rod is X=(2/3)l.

As we know that the linear density of a rod is as λ(x)= dM/dx.

So, dM = λ(x)dx

Integrate the above equation with the interval [0, l], and we get:

[tex]M=\int\limits^l_0 {\lambda(x)} \, dx \\M=\int\limits^l_0 {A(x)} \, dx \\M = A(\dfrac{x^2}{2} )\limits^l_0[/tex]

M = Al²/2   .....(1)

The rod's center of mass is measured from the left end of the rod expressed as follows:

[tex]X=\frac{1}{M} \int\limits^l_0 {x \lambda(x)} \, dx\\X = \frac{1}{M} \int\limits^l_0 {x (Ax)} \, dx\\X=\frac{1}{M}A(\frac{x^3}{3} )_0^l[/tex]

X = (1/M)Al³/3

Substitute the value of M = Al²/2 in the above equation,

X = [1/(Al²/2)]Al³/3

X = (2/3)l

Therefore, the rod's center of mass is measured from the left end of the rod is X=(2/3)l.

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The required height a car can coast up if the work done by friction is negligible and its initial speed is specified is calculated to be 33.90 m.

Initial speed of the car is given as 94 km/h.

We know that, 1 km/h = 0.277 m/s

So, u = 94 km/h = 94(0.277) = 26.038 m/s

Let the height gained by the car be h.

The final speed of the car will be zero at the height h.

v² = u²- 2 g h

So, v = 0 m/s

g = 10 m/s²

0² = 26.04²- 2 × 10 × h

20 h = 678.08

h = 33.90 m

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A basic pendulum consists of a large object suspended from a fixed support by a string.

It usually hangs vertically when it is in equilibrium. The pendulum bob is the loving name for the large object. The bob starts vibrating back and forth about its fixed equilibrium point when it is pulled out of equilibrium and subsequently released.

The motion is periodic because it is regular and keeps repeating. In an earlier section of this lesson, we discussed pendulum motion in an effort to better grasp how vibrating things work.

We revisited the topic of the oscillation of a pendulum while examining the mathematical characteristics of periodic motion.

Therefore, A basic pendulum consists of a large object suspended from a fixed support by a string.

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When they are anti-parallel to one another, the dipole has the highest electric potential energy.

Think about a dipole with charges q1 = +q and q2 = -q that is set up in the same uniform electric field as in the previous figure. There is a gap between the charges, and the electric field's strength is E.

As shown in the figure, the charges' respective forces are given as -qE and +qE.

Knowing that a dipole experiences a torque equal to, which can be expressed as  = p*E, when it is placed in a uniform electric field rather than a force,

Taking into account that the potential energy is located at the initial angle

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Awanita's power output is 8watts

When expressed as an hourly rate of electric energy delivery, power output refers to the average rate of electric energy supply during one metering interval.

To find the power output:

First we find workdone= Force × distance

Given: F=20N , d= 200cm converting to meter: (200/100)m=2m

W= 20×2=40Joules

Power,P= workdone/ time

Given: time=5seconds

P= 40/5= 8 watts

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A car moves along a straight line . The velocity of car at start will be 12m/s.

Option C is correct.

s = 12t + 3t² - 2t³

[tex]\frac{ds}{dt}[/tex] = 12 + 6t - 6t

so t = 0 then

[tex]\frac{ds}{dt}[/tex] = 12 m/s

A vector representation of the time-dependent displacement experienced by an object or particle is velocity. The meter per second (m/s) is the standard unit of velocity magnitude, which is also known as speed. Alternately, the magnitude of a velocity can be expressed in centimeters per second (cm/s).

Because velocity has magnitude as well as direction, it is a vector quantity. Speed, on the other hand, is a scalar quantity because it only has a magnitude and no direction.

Uniform velocity, variable velocity, average velocity, and instantaneous velocity are the various velocities

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The diffusivity of a gas in another gas is a measure of the rate at which the two gases mix. At room temperature (25℃), the diffusivity of a gas in another gas can be increased by a factor of 10 by raising the temperature.

The diffusivity of a gas in another gas is proportional to the square root of the temperature. This relationship is known as Graham's law of effusion. Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molecular weight. This can be extrapolated to diffusivity by assuming that the molecular weight of the two gases is similar, and that the effusion rate is proportional to the diffusivity.

Therefore, to increase the diffusivity of a gas in another gas by a factor of 10, the temperature must be increased by a factor of 10^2 = 100. This would require a temperature increase of 100 * 25℃ = 2500℃.

It is important to note that this calculation assumes that the gases are dilute and ideal, meaning that they obey the ideal gas law and do not interact with each other. In real-world situations, the diffusivity of a gas in another gas can be affected by factors such as pressure, molecular weight, and intermolecular interactions.

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52 degrees Celsius in Fahrenheit is 125.6 Fahrenheit. Temperature conversion from Celsius to Fahrenheit is done by, multiplying by 1.8 (or 9/5) and add 32.

What is Temperature?

Temperature, like any other physical quantity, is defined as the measurement of a substance's or object's warmth or coldness in relation to some standard value. While it is used to express hot and cold conditions, temperature is usually measured with a thermometer that is marked in several temperature scales, the most common of which are Celsius and Fahrenheit. There are several other temperature units.

What is SI Unit of Temperature?

According to the International System of Units, the SI unit of temperature is Kelvin, which is represented by the symbol K. In the fields of science and engineering, the Kelvin scale is widely accepted or used. However, in most parts of the world, temperature is measured using the Celsius or Fahrenheit scale.

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The ATV professional was going at a speed of approximately 2.3 km/h.

To determine the speed of the ATV professional who is racing around the track we can use the distance formula.

Distance = speed × time

Rearranging the equation we get the equation for speed as

Speed = Distance ÷ Time

Given that the ATV professional raced down 19 meters in 30 seconds time, we can calculate his speed as follows

distance = 19 meters
time = 30 seconds

Speed = 19 meters ÷ 30 seconds

Which is equal to 0.633 meters/second

This speed is expressed in meters per second (m/s). To convert this to kilometers per hour (km/h), you can multiply by 3.6 hence the final result can be formulated as

0.633 m/s x 3.6 = 2.3 km/h

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Answer:

A device that measures the amount of chemicals released into the air by a factory.

The sun provides the energy that propels water transport in plants.

Photosynthesis is the process by which plants convert light energy into chemical energy that is stored in glucose. This glucose is converted into ATP (adenosine triphosphate), which serves as an energy source for various metabolic processes in the plant, including water transport.

Water is absorbed by the plant's roots and transported upward through the stem and leaves via a process known as transpiration. This process is powered by ATP, which provides the energy required to drive water movement from the roots to the rest of the plant.

So the sun provides the energy for water transport in plants, which is converted into chemical energy through photosynthesis and stored in the ATP.

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The electric field is constant between the plates except near the edges.

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If the mass is released with an initial displacement of 2 cm then:

(a) the amplitude = 0.03184

(b) the initial velocity = 0.7779 m/s

(c) the maximum acceleration = -0314 m/s²

(d) the phase angle = -51.087°

The pace at which speed changes is known as acceleration. Acceleration typically, but not always, indicates a change in speed. Because the direction of an object's velocity is shifting even while it follows a circular course, it continues to accelerate.

The most important metric for determining an object's position and rate of movement is its velocity. The distance that an object travels in a certain amount of time might be used to define it. The object's displacement in a unit of time is referred to as velocity.

[tex]$$Solution) Maximum Velocity, $v=10 \mathrm{~cm} / \mathrm{s}$ $1 \mathrm{~cm} / \mathrm{s}=0.01 \mathrm{~m} / \mathrm{s}$$$\begin{aligned}& v=10 \times 0.01 \mathrm{~m} / \mathrm{s} \\& \mathrm{v}=0.10 \mathrm{~m} / \mathrm{s}\end{aligned}$$Period of oscillation, $\mathrm{T}=2 \mathrm{~s}$Initial displacement, $x=2 \mathrm{~cm}$$1 \mathrm{~cm}=0.01 \mathrm{~m}$$$\begin{aligned}& x=2 \times 0.01 \mathrm{~m} \\& x=0.02 \mathrm{~m}\end{aligned}$$[/tex]

[tex]$$(a) Amplitude, $A=$ ?$$\begin{aligned}& \mathrm{v}=\mathrm{A} \omega \\& \omega=\frac{2 \pi}{\mathrm{T}}=\frac{2 \pi}{2}=\pi=3.14 \\& \mathrm{v}=\mathrm{A} \omega \\& 0.1=\mathrm{A}(3.14) \\& \mathrm{A}=\frac{0.1}{3.14} \\& \mathrm{~A}=0.03184\end{aligned}$$[/tex]

[tex]$$(b) Initial velocity, $\mathrm{u}=$ ?$$\begin{aligned}& \mathrm{u}=-\omega \mathrm{A} \sin (\omega \mathrm{t}-\phi) \\& \mathrm{At}, \mathrm{t}=0 \\& \mathrm{u}=-\omega \mathrm{A} \sin (0-\phi) \\& \mathrm{u}=-\omega \mathrm{A} \sin (-\phi)\end{aligned}[/tex][tex]$$We need to find phase angle$$\\\begin{aligned}& \mathrm{x}=A \cos (\omega \mathrm{t}-\phi) \\& \text { At } \mathrm{t}=0 \\& 0.02=0.03184 \cos (-\phi) \\& \phi=-{A_{cos}\left(\frac{0.02}{0.03184}\right) \\& \phi=-51.087^{\circ} \\& \mathrm{u}=- \omega A \sin (-\phi) \\& \mathrm{u}=-3.14 \times 0.03184 \times \sin (-51.087) \\& \mathrm{u}=0.07779 \mathrm{~m} / \mathrm{s}\end{aligned}$$[/tex]

[tex]$$(c) Maximum acceleration, $\mathrm{a}=$ ?$$\begin{aligned}\mathrm{a} & =-\omega_2 . \mathrm{A} \\\mathrm{a} & =-(3.142)(0.03184) \\\mathrm{a} & =-0.314 \frac{\mathrm{m}}{\mathrm{s} 2}\end{aligned}$$(d) Phase angle,$$\phi=\text { ? }$$From part(b)$$\phi=-51.087^{\circ}$$[/tex]

Thus, If the mass is released with an initial displacement of 2 cm then:

(a) the amplitude = 0.03184

(b) the initial velocity = 0.7779 m/s

(c) the maximum acceleration = -0314 m/s²

(d) the phase angle = -51.087°

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The Lagrangian of the system can be written as L = T - U, where T is the kinetic energy of the mass and U is the potential energy. The kinetic energy T is given by [tex]T = \frac{1}{2}mv^2[/tex]

where v is the velocity of the mass. The potential energy U is given by

[tex]U = -F_0r^n[/tex]

The Euler-Lagrange equation of motion is given by d/dt (dL/dq) = dL/dq, where q is a generalized coordinate. In this case, q = r, so the equation of motion becomes:

[tex]\frac{d}{dt} \left(\frac{dL}{dr}\right) = \frac{dL}{dr} = \left(\frac{d}{dt}\right) \left(mv\right) = F = -F_0 r^n[/tex]

Conserved quantities in this system are the total energy E = T + U and the radial component of angular momentum, L = rp, where p is the radial momentum.

The effective potential energy of the system is given by

[tex]U_e_f_f = U + L^2/(2mr^2)[/tex]

The effective potential energy helps to understand the motion of the mass by including the effects of both the potential energy and angular momentum. It acts as an effective potential barrier, and the mass will move towards the origin if its total energy E is less than the minimum of the effective potential energy [tex]U_e_f_f[/tex].

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The term best describes their probability of making it Unlikely.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given,  A statistician tells a coach that his team has a 32% chance of making it to the World Series.

Since,

Thus in our case,

The term best describes their probability of making it Unlikely.

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The moment of inertia of a rod with respect to an axis perpendicular to its length and passing through its end can be calculated as follows:

I = (1/12) * mL^2,

where m is the mass of the rod and L is its length.

The moment of inertia of a point mass at a distance r from the axis of rotation can be calculated as follows:

I = mr^2.

In this case, the maximum moment of inertia occurs when the two larger weights are placed at the ends of the rod and the pivot point is placed at the middle. This way, both weights are located as far away from the axis of rotation as possible and thus contribute the maximum amount to the moment of inertia.

The moment of inertia in this case can be calculated as:

I = (1/12) * mL^2 + m_1 * (L/2)^2 + m_2 * (L/2)^2

= (1/12) * 2.2 * 1.6^2 + 0.25 * (1.6/2)^2 + 1.0 * (1.6/2)^2

= 0.53 kg m^2.

This is the maximum possible moment of inertia for this system.

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The KL46Z processor's unique datasheet and specs will determine the maximum DC current that can be pulled from an I/O pin.

The maximum DC current that may be pulled from an I/O pin on a KL46Z CPU varies based on the individual device's specs, which are shown in the datasheet for the processor. The maximum DC current that can be pulled from an I/O pin is technical information on the electrical properties and specifications of the processor included in the KL46Z datasheet. The maximum DC current is affected by a number of variables, including the power supply voltage, the processor's internal resistance, and the amount of power used by other parts. It's critical to read the datasheet in its entirety .

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The test to determine the convergence or divergence of a series is the Leibniz test for alternating series. The Leibniz test states that if the series has alternating signs.

and the terms decrease in absolute value, then the series converges. If the terms do not decrease in absolute value, the series diverges. In the series [infinity] (−1)n ln(9n) n = 2, the terms have alternating signs and the function ln(9n) increases as n increases.The test to determine the convergence or divergence of a series is the Leibniz test for alternating series. The Leibniz test states that if the series has alternating signs. This means that the terms do not decrease in absolute value, so the series diverges. Therefore, the series [infinity] (−1)n ln(9n) n = 2 is divergent.

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The man who set up the first psychology laboratory was Wilhelm Wundt

The psychology laboratories are specially designed spaces where psychology students can gather data from human subjects using the same tools as licensed psychologists.

It can be noted that in 1879, Wundt founded the first psychological laboratory of the world in Leipzig, Germany, where he mainly studied sensations and feelings by employing experimental methods.

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The combined moment of the two forces about ;Moment about point O = 0

,Moment about point C = 52 lb · 8 ft = 416 lb · ft,Moment about point D = 52 lb · 4 ft = 208 lb · ft.

Force is an influence that causes an object to move, stop, or change its direction. It can be a push or pull, and can result from interaction with another object, person, or object of nature. Force can also be caused by non-contact interactions such as electric fields, magnetic fields, and gravitational forces. Force can be measured in Newtons, which is the amount of force required to accelerate a one-kilogram mass by one meter per second squared.

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Nickel-60 is made of 28 protons and 32 neutrons.

The mass defect = [tex]9.14 x 10^-25 grams.[/tex]

The mass of a body is a natural property. It was widely believed, prior to the discovery of the atom and particle physics, to be connected to the volume of matter in a physical body. It was found that different atoms and elementary particles, although theoretically having the same amount of matter, have different masses.

Different but physically equivalent conceptual definitions of mass are used in modern physics. Experimental definitions state that a body's mass is a measure of its inertia, or resistance to acceleration (change in velocity), when a net force is applied. An object's mass also affects the gravitational pull it exerts on other bodies.

There are 28 protons and 32 neutrons in nickel-60.

28 x 1.00728 = 28.20384 amu

32 x 1.00867 = 32.27744 amu

adding above = 60.48128 amu

subtract Ni = -59.9308 amu

mass defect = 0.55048 amu

1 amu =[tex]1.66053886 × 10^-24 grams[/tex]

So the mass defect = [tex]9.14 x 10^-25 grams[/tex]

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Answer:

To determine the distance traveled in 22 seconds, we can use the formula:

distance = speed * time

First, we need to convert the speed from km/hr to m/s, which is the standard unit for measuring speed in physics.

1 km/hr = 1000/3600 m/s = 5/18 m/s

So, 650.0 km/hr = 650.0 * 5/18 m/s = 130.9 m/s

Next, we can calculate the distance traveled in 22 seconds:

distance = speed * time = 130.9 m/s * 22 s = 2860.8 m

So, the plane has traveled 2860.8 meters in 22 seconds.

Explanation:

If high temperature gas enters compressor, than although the compressor's capacity declines with increasing superheat, its current consumption reduces because less vapour is drawn in during the suction stroke.

A compressor is a mechanical device that lowers a gas's volume while raising its pressure. An air compressor is one distinct case of gas compressor. Two very different pumps and compressors can convey a fluid through a pipe while increasing the fluid's pressure.

The molecules in a hot gas move more quickly than those in a cold gas; while the mass of the gas doesn't change, the kinetic energy does, which raises the temperature.

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To calculate Larry's average velocity during two intervals, we need information on his displacement (change in position) and time during those intervals. The average velocity is given by the formula:

v = Δx / Δt

where Δx is the displacement and Δt is the time.

Without knowing the specific values for Δx and Δt, it is not possible to calculate Larry's average velocity during each of the two intervals.

It is important to note that velocity is a vector quantity that includes both magnitude and direction. The displacement Δx must be in the same direction as the velocity, while the time Δt must be positive.

If the direction of motion changes during the interval, then the average velocity will be different for each interval and will not necessarily be equal to the final velocity.

In conclusion, to calculate Larry's average velocity during two intervals, we need to know the displacement and time during those intervals. The formula for average velocity is given by v = Δx / Δt, where Δx is the displacement and Δt is the time. Without knowing the specific values for Δx and Δt, it is not possible to calculate Larry's average velocity.

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Without the nutcracker, Luisa would have to use significantly more force to crack the walnut. Because the nutcracker acts as a lever, the force applied to the handles is multiplied by the force applied to the walnut.

The mechanical advantage is 11.7 cm / 0.3 cm = 39 because the lever arm length is 12 cm - 0.3 cm = 11.7 cm.

This means that the force on the walnut is 39 times the force on the handles, or 21 N x 39 = 819 N. This is a much greater force than the 21 N applied to the handles with the nutcracker, implying that Luisa would have to work much harder to crack the walnut without it.

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So the speaker's power output is approximately 2773.99 watts.

The power output of a speaker can be calculated from the sound intensity level and distance using the equation:

P = 10^(I/10) / (4 * pi * d^2)

where P is the power output in watts, I is the sound intensity level in dB, and d is the distance in meters. Substituting the given values, we get:

P = 10^(108/10) / (4 * pi * 17^2)

P = 10^10.8 / (4 * pi * 289)

P = 3162277.7 / (4 * pi * 289)

P = 3162277.7 / 1140

P = 2773.99 W

A motor's output power is calculated by multiplying its torque output by the angular velocity of its output shaft. The power lost by an electrical component in a circuit is also a function of the voltage across the component and the current that flows through it.

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The technique in the above image is a form of asexual reproduction (option A).

Reproduction is the act of making copies of new individuals biologically.

Asexual reproduction is a type of reproduction which a new offspring is produced by a single parent. The new individuals produced are genetically and physically identical to each other.

Asexual reproduction is observed in both multicellular and unicellular organisms. According to the image attached above, a cutting of a parent plant is used to produce a new organism, hence, is a form of asexual reproduction.

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The volume of a 25 ft x 10 ft x 12 ft cargo container is 111.1 cubic yards (3000 cubic feet divided by 27).

Volume is the three-dimensional space occupied by an object or a substance. It is the measure of the amount of space an object takes up and is typically expressed in units such as cubic centimeters, cubic meters, cubic feet, or cubic yards.

The volume of the cargo container can be found by multiplying its length, width, and height:

V = 25 ft × 10 ft × 12 ft = 3000 ft³

To convert from cubic feet to cubic yards, divide by 27:

Volume calculation: 111.1 yd³ = (3000 ft³ / 27).

So the volume of the cargo container is 111.1 cubic yards.

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Explanation:

The gravitational force between two masses, m1 and m2, separated by a distance, r, can be calculated using the formula:

F = G * (m1 * m2) / r^2

where

F is the gravitational force,

G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2),

m1 is the mass of the first object,

m2 is the mass of the second object,

r is the distance between the centers of the two objects.

Plugging in the values:

F = G * (7.34 x 10^22 kg * 5.97 x 10^24 kg) / (3.88 x 10^8 m)^2

= (6.67 x 10^-11 Nm^2/kg^2) * (4.36 x 10^47 kg^2) / (15.0244 x 10^16 m^2)

= 2.80 x 10^22 N

So, the moon produces a gravitational force of 2.80 x 10^22 N on the Earth when their centers are 3.88 x 10^8 meters apart.

The required intensity of laser beam when light power and diameter are given is calculated to be 1.875 × 10³ w/m².

Power of light is given as 1.2 mw = 1.2 × 10⁻³ w

Diameter of the beam is given as 0.90 mm = 0.9 × 10⁻³ m

So, area = (π d²)/4 = π (0.9 × 10⁻³)²/4 = 0.64 × 10⁻⁶ m²

Now let us calculate the intensity of the beam, it is given by the formula, I = P/A

where, P is power

A is area

Putting values in the above equation, we have,

I = P/A = (1.2 × 10⁻³)/(0.64 × 10⁻⁶) = 1.875 × 10³ w/m²

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