a long straight conductor has a circular cross section of radius r and carries a current i. inside the conductor, there is a cylindrical hole of radius a whose axis is parallel to the axis of the conductor and at a distance b from it.

50 dayss  long will it take for a sample of chromium-51 to decay from 35. 0 grams to 10. 0 grams

Observationally stable chromium isotopes include chromium Cr-51.

It is utilized as a diagnostic radiopharmaceutical agent when injected intravenously to calculate the volume or mass of red blood cells, research red blood cell survival, and assess blood loss.

Introduction.With a half-life of 27.7 days and gamma rays with a maximum energy of 0.320 MeV, chromium-51 is a widely utilized radionuclide

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The two light bulbs are to be resolved at a distance of 60.1 km.

The formula of Rayleigh criterion for the diffraction limit is

[tex]\theta \:=\: 1.22 \: \frac{\lambda}{D}[/tex]

where

Because in problems didn't give the detail about the wavelength, for visible light the radiation wavelength is 750 nm - 400 nm. In this problems I assume λ = 600 nm = 600 × 10⁻⁹ m = 6 × 10⁻⁷ m

[tex]\theta \:=\: 1.22 \: \frac{\lambda}{D}[/tex]

θ D = 1.22 λ

θ × 4.00 × 10⁻² = 1.22 × 6 × 10⁻⁷

θ = (7.32 × 10⁻⁷) ÷ (4.00 × 10⁻²)

θ = 1.83 × 10⁻⁵ rad

The angle for the light bulbs

[tex]\theta = \frac{s}{r}[/tex]

where

s = θr

r = 1.1 ÷ (1.83 × 10⁻⁵)

r = 6.01 × 10⁴ m

r = 60.1 km

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2.23 seconds is the cannons' total flight time.

What is Acceleration due to gravity ?

The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity. M/[tex]s^{2}[/tex] is its SI unit. Both magnitude and direction are present.

According to the information

A diagonal ball is launched at a 45° angle from the horizontal. The ball is being fired in a projectile motion. A projectile is a motion in which a body that has been discharged into space with a velocity U is allowed to fall freely while being affected by gravity.

The cannon ball's total flight time, T, can be represented as;

where T = 2Usin(theta)/g;

U is the ball's starting speed, which is 35 m/s.

The angle the ball makes with the horizontal is theta, which is equal to 45°.

The acceleration caused by gravity is g =  9.81 m/[tex]s^{2}[/tex]

Incorporating the provided data into the existing formula;

T = 35sin45°/9.81

T = 35×0.7071/9.81

T = 24.74/9.81

2.52 seconds later

2.23 seconds is the cannons' total flight time.

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From a ceiling, a rope with the mass m and length L hangs. Demonstrate that v =√gy is the wave speed on the rope at a distance of y above the lower end.

The amount of space a wave covers in a certain amount of time, such as the number of meters it covers in a second, is known as its wave speed. Speed = Wavelength x Frequency is an equation that describes how wave speed relates to wave wavelength and wave frequency. When the wavelength and frequency are known, this equation can be used to determine the wave speed. Wave frequency (f) is recorded in hertz, while wave speed (v) is measured in meters per second (m/s) (Hz)

Although technically, velocity means both speed and direction, wave velocity is most often used to refer to speed. A wave's velocity is independent of its intensity and equal to the product of its wavelength and frequency (number of vibrations per second).

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The system's behavior becomes more elastic when the spring constant, k, is increased, as is the Q factor

Since a spring's constant k and its length are inversely related, when a spring is divided into n parts, the length increases by 1n, making the spring constant k/(1/n)=nk.

The square root of the mass and the spring constant have opposite relationships with respect to the period of a spring-mass system.

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Answer:

Explanation:

You can drive at 60 miles per hour

D = 60 miles

t = 1 hour

Speed:

V = D / t = 60 / 1 = 60 mph

Proton will undergoes the lesser acceleration

Due to the opposite polarity of an electron and a proton, when they are in an electric field, they are attracted to one another by an electrical force of equal strength. However, because of their opposing charges, the force's direction will be the opposite.

An electron will accelerate more quickly than a proton because of the difference in mass between the two particles.

Thus, the electric forces acting on them will be equal in strength but directed in the opposite direction. Since the mass of the proton is 1836 times greater than the mass of the electron, its acceleration will be [1/1836] times greater.

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The ball falls to the ground with a magnitude of 244.8 feet and a speed of 91.0 feet per second.

In this situation, we have a three-dimensional problem that kinematics can help us solve by determining the position, velocity, and acceleration of the body.

The vector, which is the ball's position in the air at time t,

p(t) = (60 i + 64 k) t + 1/2 (-6 j - 32 k) t ²

and its velocity is given by

v(t) = (60 i + 64 k) + (-6 j - 32 k) t

The time the ball is in the air is equal to the time it takes for the position vector's vertical (k) component to reach zero, so we solve,

64 t - 32/2 t ² = 0  ==>  t = 0 OR t = 4

and so the ball is in the air for 4 s.

The ball has position vector.

p(4) = (60 i + 64 k) t + 1/2 (-6 j - 32 k) t ² = 240 i - 48 j

which has magnitude.

||p(4)|| = √(240² + (-48)²) = 48 √26 ≈ 244.8 ft

in the direction of the positive x axis in the x, y plane so that

tanθ = -48/240 = -1/5  ==>  θ = -arctan(1/5) ≈ -11.3º

or 11.3º South of East.

The ball swiftly strikes the ground.

||v(4)|| = ||60 i - 24 j - 64 k|| = √(60² + (-24)² + (-64)²) = 4 √517 ≈ 91.0 ft/s.

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Answer: The electrician need78 feet of wire are required by the electrician as a result.

Reason:

The elevated angle between the horizontal plane and line of sight to the connection on the pole.

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The change in momentum of the bowling ball of mass 8.11 kg is 159.152 kgm/s.

The change in the momentum is equal to the product of the mass and the change in the velocity.

To calculate the change in momentum of the bowling ball, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the change in momentum of the ball is 159.152 kgm/s.

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Complete question: A force of 203 N is exerted on 8.11 -kg bowling ball over time span of 0.784 seconds. Calculate the change in momentum of the bowling ball

Yes, it is possible to have the larger force produce less torque than the smaller force. It is possible for the larger force to be applied closely enough to the center of mass of the rigid body due to which its resulting torque is smaller than that of a smaller force applied at a point far from the center of mass.

Force is an external cause due to which a body tends to modify or change its state. Due to application of force, the body can also change its size, shape, and direction. Force has both direction and magnitude.

Force = mass × acceleration

The force that can cause an object to rotate along an axis is measured as torque.

[tex]\tau = rF\sin\theta[/tex]

Here, [tex]\tau \\[/tex] = Torque

r = radius

F = force

[tex]\theta[/tex] = the angle between the F and the lever arm

In the given question, lets assume the following,

F = Large force

d = Distance from the point of application of the large force to center of mass

f = Small force

D = Distance from the point of application the of small force to center of mass

Now,

Assuming D > d (i.e, D is greater than d).

The torque caused by the large force is Fd, and the torque caused by the little force is fD if the forces are applied perpendicular to the body's axis. Hence, depending on the values of F, f, D, and d, we can have Fd < fD.

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She draws her arms close to her body, decreasing her moment of inertia, to quicken the rotational velocity of her spin. Due to the conservation of angular momentum, rotational velocity will increase,

The angular velocity (w), a vector quantity in uniform circular motion, is determined by dividing the angular displacement (ΔФ a vector quantity), also a vector quantity, by the change in time (t). Speed is equal to the arc length travelled (S) divided by the change in time (Δ), which is also equal to ||R.

According to the above given information

We got to know that

She draws her arms close to her body, decreasing her moment of inertia, to quicken the rotational velocity of her spin. Due to the conservation of angular momentum, rotational velocity will increase.

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The value of resistance r is 100ohm

Define resistance.

The opposition a substance provides to the flow of electrical current is referred to as resistance. The capital letter R is used to symbolize it. The ohm, which can be written as a word or represented by the Greek letter omega  Ω in uppercase, is the universal unit of resistance.

Because the output current of the first resistor flows into the input of the second resistor in a series circuit, the current through each resistor is equal. All of the resistor leads on one side of the resistors are connected together, as are all of the leads on the other side, in a parallel circuit.

In a parallell circuit,

1/R =  1/R1 + 1/R2

Given R1= r

          R2= 400

          I= 5

          V= 12V

1 / R + 1 / 400 = 5 / R

1 / 400 = 4 / R

R = 400/4

R= 100ohm

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The reason padded dashboards are used in cars is that they a.) change the impulse in a collision. Therefore option a) is correct.

Padded dashboards make automobiles safer as they increase the time taken to decrease the momentum of impacting body to zero, which also decreases the impact. Therefore, force acting on the padded dashboards is small.

If the driver or passenger hits the dashboard, then the force and time required to stop the momentum is exerted by the dashboard. Padded dashboards serve to extend the time duration of the impact, hence minimizing the effect of the force.

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A capacitor and a resistor in series. This is known as a low-pass filter, and it attenuates higher frequencies more than lower frequencies, so at a given voltage the current will not depend on the frequency.

What is frequency?
In physics, frequency is the amount of waves that pass a fixed point in a unit of time as well as the number of cycles or vibrations that a body in periodic motion experiences in a unit of time. After moving through a series of situations or positions and then returning to its initial position, a body in periodic motion is thought to have experienced one cycle or one vibration. See also simple harmonic motion and angular velocity.

The frequency is 2 per second if the period, or time interval, needed to complete one cycle as well as vibration is 1/2 second; it is 100 per hour if the period is 1/100 of an hour. In most cases, the frequency is equal to the period, or time interval, reciprocally, so frequency = 1/period = 1. (time interval).

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The statement that is true is that; nuclear fission is used to produce electric power in nuclear reactors.

We know that a fission reaction has to do with a kind of reaction in which a radioactive nucleus is bombarded by the use of a particle and then there is the disintegration of the atomic nucleus in order to produce energy.

This has been one of the ways by which we can be able to generate electricity in several power plants across the world. The loss in the mass of the reactants is the equivalent of the energy produced.

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The angular displacement of each wheel during this period will be 209 rad

Explain angular displacement

A body's angular displacement is the angle (measured in radians, degrees, or revolutions) by which a point rotates around a specific axis or center in a particular way. Because a body rotating about its axis experiences variable velocities and accelerations at all times, the motion cannot simply be considered as a particle motion (t).

We must first assume that the car's wheels are not slipping in relation to the pavement. If so, we can infer that the angular velocity and acceleration are given by

w = v/r = (20m/s)/(.300 m) = 6  rad/s

a = a/r = (1.5 m/s2)/(.300 m) = 5 rad/s2

Using this data, we can calculate the angular displacement by:

angular displacement = (6 rad/s)(8.00 s) + .5(5 rad/s2)(8.00 s)2

                                      = 48 rad + 160 rad = 209 rad

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A dwarf ellipse. Despite being incredibly difficult to view, astronomers recently realised that this form of galaxy may be quite common.

What is a galaxy?

A galaxy is a vast collection of stars, solar systems, gas, and dust. Gravity holds a galaxy together. There is also a black hole at the centre of our galaxy milkyway.

Dwarf On a smaller scale, elliptical galaxies seem to share many of the same global characteristics as typical elliptical galaxies. They lack recent star formation, are elliptical in shape, and have very little to no gas. The most prevalent type of galaxy in the cosmos is a dwarf galaxy, but because of their small size, low mass, and low luminosity, they are hard to find.

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Ideally, the water bounces off the turbine blades, maximizing electricity era. when water splashes, momentum changes extra than while you are simply status.

Also, if the change in momentum of the water is greater than the alternate in momentum of the blade, the blade will spin faster. Consistent with the laws of movement, the momentum of the center of gravity of an object can most effective be changed by the movement of an external force.

But, because of the frictional force generated while the tires contact the ground, the internal force of the engine is added, allowing the automobile to accelerate.

Hydro turbines convert the strength of flowing water into mechanical energy. A hydroelectric generator converts this mechanical power into energy. A high stress water jet is pressed towards the turbine blades. The route of flow modifications. The ensuing change in momentum exerts a force on the turbine blades, inflicting the turbine to rotate.

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If three capacitors with values of each are connected in series, the corresponding capacitance is 46 mF 1 / (1/1.)+(1/1.5)+(1/2.).

An electrical energy storage device is a capacitor. It has two conductors in it that appear to be close to one another but are kept apart. A straightforward example of a particular storage device is the parallel-plate capacitor.Equivalent Capacitance for three capacitors in series can be given by the following equation. 1/C = 1/C1 + 1/C2 + 1/C3.

Capacitors are most frequently used for signal coupling and decoupling, power conditioning, electronic noise filtering, energy storage, and remote sensing. Capacitors are employed in many different industries since they have a crucial and adaptable role for a variety of applications.

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Answer:

V = 2.86 m/s

Explanation:

Given:

m = 1400 kg

p = 4000 kg·m/s

_________________

V- ?

Momentum:

p = m·V

Velocity:

V = p / m

V = 4000 / 1400 ≈ 2.86 m/s

Yes It is conceivable for a force to produce less torque when it is greater than a force that is smaller.

An object's motion can be altered by unbalanced forces.Two things cause this.An object will move if an imbalanced force pushes and pulls on it while it is at rest.Unbalanced forces also can cause an item in motion to shift its speed or direction.

Students are aware that unbalanced forces can cause objects to accelerate, decelerate, or change direction during their motion.

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Force required is: -170N for the distance of 342.25m.

a) F=ma

F= - 85×2.0 = - 170

b) using energy

5×85×37²=170×d

d = 342.25 m

c) The work done would be given by

W= F×d

W  =(−1.7×10²N)×(3.4×10²)

W=−5.8×[tex]10^{4}[/tex]J

d) The net force on the mass would be

F = ma

F = -340 NF

-ve sign indicates that the force acts opposite to the direction of motion.

e) Using the kinematic equation

v²= u² + 2ad

d= 1.7 × 10² m

f) The work done would be given by

W= F×d

W= -5.8 × [tex]10^{4}[/tex]

-ve sign indicates that the energy of the rider decreases by the force

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The sequence for de broglie wavelengths from largest to smallest is electron > proton > helium.

de broglie wavelength is an important concept to study various phenomenon in quantum mechanics.

Where, h is the Plank's constant

m is the mass of the particle

v is the velocity of particle.

mass of proton = mp = 1.6 x [tex]10^{-27}[/tex] kg

mass of electron, me = 9.1 x  [tex]10^{-31}[/tex] kg

mass of helium nucleus, mHe = 6.6 x  [tex]10^{-27}[/tex] kg

As the velocity of all the three elements are same as v.

According to the de Broglie wavelength formula, since v is same for all λ is inversely proportional to the mass of the element.

Lesser  the mass more will be the de broglie wavelength.

Here, mass of electron < mass of proton < mass of helium nucleus.

So, de broglie wavelength of electron > de broglie wavelength of proton > de broglie wavelength of helium nucleus.

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Two vectors vector a and vector b, each located in a different position in the plane, have equal magnitude and the same direction, both vectors are considered to be parallel to each other.

Two vectors are said to be parallel if and as it were in case the angle between them is degrees. Parallel vectors are too known as collinear vectors, that is two parallel vectors will be continuously parallel to the same line but they can be either within the same direction or within the exact inverse direction. The cross product of any two parallel vectors could be a zero vector. For any two parallel vectors a and b, their dot product is equal to the product of their magnitudes.

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On the north pole, one day for about 17 hours on uranus.

Its call is a reference to the Greek god of the sky, Uranus, who, in step with Greek mythology, was the extremely good grandfather of Ares, grandfather of Zeus, and father of Cronus.

Uranus is the only planet whose equator is sort of at a proper attitude to its orbit, with a tilt of 97.77 degrees – likely the end result of a collision with an Earth-sized item lengthy in the past.

The blue-inexperienced color effects from the absorption of crimson light by way of methane gas in Uranus' deep, cold, and remarkably clean surroundings.

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Work done by team A while pulling team B is 2200 J.

What is work done?

The work done by a force is defined to be the product of the component of the force in the direction of the displacement and the magnitude of this displacement. Formula. Work can be calculated by multiplying Force and Distance in the direction of force as follows. W = F × d.

What is cos theta in work done?

Work done in physics is defined as a dot product of a force vector and displacement vector. W = F.S.cos θ where cos θ is the angle between the force vector and displacement vector.

What force is applied during tug of war?

Tug-of-war is a game that uses friction as the driving force.

What happens in a tug of war if both teams apply equal force?

In a tug of war, if the two teams are applying equal force on the rope then the net force acting on the rope is zero and hence the rope stays at the same place.

Force F= 1100 N

Displacement caused by the applied force S = 2 m

Force and displacement are in the same direction the angle between them is zero.

Work done is calculated as

[tex]W=F * S * cos theta\\W=1100 * 2 * cos 0\\W=2200 J[/tex]

Thus, the work done by team A to pull is 2200J.

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Boyle's law states that the volume of a given quantity of gas sustained at a fixed temperature is inversely proportional to the measurement's measurement of pressure.

The motion of an item is related to the forces operating on it by Newton's equations of motion. According to the first law, until a force strikes on an item, it will not alter its motion. According to the second law, an object's force is determined by multiplying its mass by its acceleration. According to the third law, when two objects interact, they exert equal-sized and opposite-direction pressures upon one another.

Static pressure plus dynamic pressure equals total pressure is a simple way to express Bernoulli's equation. Each point Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own unique static pressure p and dynamic pressure q.

Joseph-Louis Gay-Lussac investigated the expansion of gases as the temperature is increased. His data helped establishCharles' law, which says, in its modern form, that the volume of a gas is directly proportional to the absolute temperature.

Now we need to say which law is there which state that at a fixed temperature, pressure and volume of a gas are inversely proportional.

The law that states this is Boyle's law.

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It is given that:

dependent source = A-0.2Vo