In the photoelectric effect, suppose that the intensity of the light is increased, while the frequency is kept constant. The frequency is greater than the minimum frequency fo. State whether each of the following will increase, decrease, or remain constant, and explain your choice: (a) the current in the phototube, (b) the number of electrons emitted per second from the metal surface, (c) the maximum kinetic energy that an electron could have, (d) the maximum momentum that an electron could have, and (e) the minimum de Broglie wavelength that an electron could have.

In one-third of all collisions between motorbikes and cars, the car driver claims he simply did not notice the motorcycle. when both the suspect and officer automobiles were totaled as a result.

Of pit maneuvers performed by professional officers. A police car is usually fortified for this and is heavy. It's likely that a light vehicle attempting a pit maneuver will sustain significant damage. If a novice tried this, they would probably get it incorrect and make a worse hazard. Officers and bystanders may potentially suffer damage as a result. The police are unsure of your intentions—whether you're trying to assist them for collisions, the suspect, or a different criminal who wants to hurt him or her. You'll be charged with several crimes due to speed, including obstruction and assault with a deadly weapon, for this action.

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The name of the mineral with the following physical characteristics is the Harder Than, according to the above mineral identification table. Glass. Two directions are not at 90 degrees. black or dark green vitreous luster. 124 and 56 degree cleavage planes are present. Hornblende. Cleavage.

Non-Metallic. Metallic minerals are those that include metal elements in their unprocessed state. Non-metallic minerals are those that don't include any metals. Melting metallic minerals produces a new material. Non-metallic minerals undergo such a process, but no new product is produced. Nonmetals are chemical elements in chemistry that often don't have a lot of metallic characteristics; they can be anything from colorless vapors to glossy solids. Nonmetals' electrons behave differently from those of metals.

Hydrogen, carbon, nitrogen, oxygen, phosphorus, sulfur, silicon, boron, tellurium, and selenium are among the non-metallic elements in the periodic table. They also consist of noble gases and halogens (such as fluorine, chlorine, bromine, iodine, and astatine) (helium, neon, argon, krypton, xenon and radon). The least metallic element among F, Cl, Br, and At is fluorine. This is true because metallic character grows down the group and lessens over time.

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The circuit has an unknown impedance z. But we do know that the source delivers an apparent power of 50va with a power factor of 0.8 lagging. The Unknown Impedance Z is 108 Ω 20/0°.

Formula of Impedance = Z= under root R2 + (Xl - Xc)2

Z = impedance

R = resistance

XL = inductive reactance

XC = capacitive reactance

After putting the values in formula we get 108 Ω 20/0°.

Impedance, which is produced in a circuit by the interaction of resistance and reactance, is the resistance to alternating current. The impedance of a two-terminal circuit element can be calculated as the ratio of the complex representation of the sinusoidal voltage between its terminals to the complex representation of the current flowing through it.  Typically, it is dependent on the frequency of sinusoidal voltage. Impedance extends the concept of resistance to alternating current (AC) circuits and has both magnitude and phase, in contrast to resistance, which only has magnitude. The idea of impedance is crucial when doing an AC analysis of electrical networks because it makes it possible to link sinusoidal voltages and currents by a simple linear law. The impedance matrix nevertheless shows a linear relationship between the complex voltages at the ports and the currents flowing through them, despite the fact that the two-terminal definition of impedance in multiple port networks is inadequate. The siemens is the SI unit for admittance, which is the inverse of impedance and was formerly known as the mho. Instruments used to measure electrical impedance are called impedance analyzers.

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The distance in meters from the top of the pendulum is 0.9939 m and Yes the equation will beT= 2pi * sqrt ( I / mgd).

A simple pendulum consists of a mass m hanging at the end of a string of length L. The period of a pendulum or any oscillatory motion is the time required for one complete cycle, that is, the time to go back and forth once.

If the amplitude of motion of the swinging pendulum is small, then the pendulum behaves approximately as a simple harmonic oscillator, and the period T of the pendulum.

Periodic Motion is based on the concept of periodic motion. Periodic motion can be defined as any motion that repeats over and over again with the same time required for each recurrence. A period is the amount of time for the system to complete one cycle.

In this example, it is the amount of time for the energy sphere to be released and then return to its approximate release point. The frequency is the number of cycles per unit of time, i.e., how many cycles are completed in one minute.

Given,

length = 1.25 m

mass =1.23 kg

T = 2πsqrt(l/g)

2 = 2 *3.14 sqrt(l/9.8)

l = 0.9939 m

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The  combinations of the rocket mass Mrocket and force from its thrusters FThrusters would result in an upward acceleration of 2 m/s2  are

A. Mrocket 1 kg, FThrusters 12 N

C. Mrocket 3 kg, FThrusters 6 N

Using Newton's Second Law, F = ma, we can determine the force needed to accelerate a rocket at a given rate. Since the mass of the rocket is given, we can calculate the force by rearranging the equation to F = m*a, where m is the mass and a is the acceleration. Therefore, for a mass of 1 kg, the force needed to achieve an acceleration of 2 m/s2 is 12 N. Similarly, for a mass of 3 kg, the force needed to achieve an acceleration of 2 m/s2 is 6 N.

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Xc = (0.467 - 0.427j)R is the original capacitive reactance in terms of r.in an rlc circuit that includes a source of ac current operating at a fixed frequency and voltage, the resistance r is equal to the inductive reactance

Since the resistance in the circuit is R, the reactance of the inductor is XL and the reactance of the capacitor is XC, then the impedance of the circuit is

Z = √[R² + (XL - XC)²]

Since the inductive reactance XL equals the resistance R, we have that

Z = √[R² + (XL - XC)²]

Z = √[R² + (R - XC)²]

Thus, the current in the circuit is thus I = V/Z = V/√[R² + (R - XC)²]

Now, when the plate separation of the parallel plate capacitor is reduced to one-half its original value, the current doubles. Also, when the plate separation is reduced to half, the capacitance doubles since C ∝ 1/d where C is capacitance and d separation between the plates. Since the capacitance doubles, the new reactance XC' is twice the initial reactance XC. So, XC' = 2XC. Thus the new impedance is thus

Z' = √[R² + (R - XC')²]

Z' = √[R² + (R - 2XC)²]

The new current is I' = V/Z' = V/√[R² + (R - 2XC)²]

Since the current doubles, I' = 2I.

V/√[R² + (R - 2XC)²] = 2V/√[R² + (R - XC)²]

1/√[R² + (R - 2XC)²] = 2/√[R² + (R - XC)²]

√[R² + (R - XC)²] = 2√[R² + (R - 2XC)²]

squaring both sides, we have

[R² + (R - XC)²] = 4[R² + (R - 2XC)²]

expanding the brackets, we have

[R² + R² - 2RXC + XC²] = 4[R² + R² - 4RXC + 4XC²]

[2R² - 2RXC + XC²] = 4[2R² - 4RXC + 4XC²]

2R² - 2RXC + XC² = 8R² - 16RXC + 16XC²

collecting like terms, we have

16RXC - 2RXC + XC² - 16XC² = 8R² - 2R²

14RXC - 15XC² = 6R²

15XC² - 14RXC + 6R² = 0

Using the quadratic formula to find XC, we have

Since it is capacitive, we take the negative part.

So, Xc = (0.467 - 0.427j)R

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Charles' law stipulates that the volume of a given amount of gas is exactly related to its temperature on the kelvin scale while the pressure is held constant.

What is nitrogen most frequently used for?

On nitrogen, the chemical industry depends. It is used to make fertilizers, dyes, nylon, nitric acid, and explosives. To make these products, nitrogen must first be coupled with hydrogen to make ammonia. For this, the Haber process is employed.

Is nitrogen bad for people?

People lose their lives every year by breathing "air" with insufficient oxygen. Many people believe nitrogen gas is safe because it makes up 78 percent of the air we breathe. However, breathing nitrogen is only safe when it is combined with the right proportion of other gases.

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Heat capacity on its own is rarely enough to predict the thermal performance of a material. Another important consideration is conductivity. If each material was made into a frying pan, Copper (k=398 W/mK) expect to be heated the most uniformly in a short period of time.

The amount of heat that must be delivered to an object in order to result in a unit change in temperature is referred to as an attribute of matter known as heat capacity or thermal capacity. The SI unit of heat capacity is joules per kelvin (J/K). Heat capacity is a general attribute. The comparable intensity property is the specific heat capacity, which is determined by dividing an object's heat capacity by its mass. By dividing the heat capacity by the substance's molecular weight, the molar heat capacity may be calculated. The volumetric heat capacity measures the heat capacity per volume. Architecture and civil engineering frequently refer to a building's capacity to store heat as having "thermal mass." The variance can be ignored when working with materials under confined pressure and temperature ranges. When measured at a starting point of 25 °C and 1 atm of pressure, one pound of iron, for example, has a heat capacity of roughly 204 J/K. It is adequate for temperatures between 15 °C and 35 °C and for ambient pressures between 0 °C and 10 °C because the real value fluctuates so little in those ranges.

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The time taken for the wave on the string to travel from the centre of the circle of the ball is 6.5 * 10⁻⁶ s.

Given that, mass of the ball mb = 18.1 kg

Angular speed of the ball ω = 12.5 rad/s

Mass of the string ms = 0.0184 kg

Speed of the wave of the string is given by the formula,

sw = √(Ts / m')  -------(1)

where, Ts is tension in the string

m' is mass per unit length of the strength

Ts = mb * ω² * l  --------(2)

m' = ms/l ---------(3)

Substituting (2) and (3) in (1), we have

sw = √(mb * ω²* l²/ ms) ----(4)

We know that, t = l / sw -----(5)

Substituting (4) in (5), we have

t = √( ms/ mb *ω²) = √( 0.0184/(18.1 * 12.5²)) = √( 0.0184/2828.125)

= 0.0000065 = 6.5 * 10⁻⁶ s

Thus, the time taken for the wave on the string to travel from the centre of circle to the ball is 6.5 * 10⁻⁶ s.

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Number of moles of air that leave the house during the daytime is 1154.017 moles.

The pressures are constant so:

V₁/T₁ = V₂/T₂

Given,

During the night, V₁ = 900 m³, and T1₁= 288K.  

During the day, T₂ = 297K, and V₂ =?

V₂ = V₁*T₂/T₁ = 900*297/288 = 928.125 m³

928.125 - 900 = 28.125 m³

Volume of air that leave the house during the daytime = Vₐ

V₂/T₂ = Vₐ/Tₐ

Vₐ = V₂*Tₐ/T₂ = 28.125*273/297 = 25.85 m³

To calculate the number of moles,

22.24 liters per mole, and 1000 liters per m³, so

number of moles = N

N = 25.85*1000/22.4

N = 1154.017 moles.

Therefore, number of moles of air that leave the house during the daytime is 1154.017 moles.

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The equilibrium position of the electron at the center of the nucleus is  R  = 3.16 x10⁻¹⁰m.

Thomson discovered the electron and proposed a structural model of the atom. His research also led to the invention of the mass spectrometer. Thomson announced that he discovered that atoms are made up of smaller components.

Calculation:-

K = 2.304 × 20^-²⁸ / 3

f = 1/2π√k/m

4.63 × 10¹⁴ = 1/2× 3.141 √2.304 × 20^-²⁸ / R³ (9.1 × 10-31)

R = 3.16 x10⁻¹⁰m.

This discovery revolutionized the way scientists think about atoms and had a major impact on the field of physics. Thompson called them corpuscles but what he found are now commonly known as electrons. The plum pudding model is defined by an electron surrounded by a volume of positive charge like a negatively charged plum embedded in a positively charged pudding.

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Greenhouse gases are gases that are present in the Earth's atmosphere and trap heat from the Sun, preventing it from radiating back out into space. Human activities that release greenhouse gases into the atmosphere can contribute to global warming. Two examples of such activities are:

Overall, human activities that release greenhouse gases into the atmosphere are a major cause of global warming. These activities can have serious consequences for the Earth's climate and can impact many aspects of human life.

When an object's internal energy is:... really when its temperature is higher than that of its surroundings, it will typically be a net radiator of energy.

From one thing to another, heat energy can be exchanged. Heat is the flow or transfer that occurs as a result of the temperature differential between two objects.

Heat is a means of transferring energy to and from molecules. Atoms and molecules accumulate thermal energy as the temperature rises, which leads them to move faster and further apart. When the temperature drops, atoms.

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Mutation caused genetic drift and decreased fitness and Sequence alteration in the genomic DNA is the fuel driving the course of evolution.

Mutations, or changes in the nucleotide sequence, can result fromerrors during DNA replication, from covalent changes in structure because of reaction with chemical or physical agents in the environment, or from transposition. Most of the sequence alterations are repaired in cells.

Without such mutations, no changes would occur in populations of species to allow them to adapt to changes in the environment. Mutation is the sudden change in the DNA. Mutations arise due to any kind of mutagen or radiation. In this disaster mutations were introduced due to the radiations. So, there will be variations in the organism.

Mutations will not cause changes only in the physiology of an organism. It does not cause genetic drift and decreased fitness. New alleles cannot be fixed by mutations.But mutations can definitely increase the variety of organisms.

Hence, the correct option is d.

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The total positive charge stored on the two capacitors is;

4kQ₀/(k + 1)

We are told that the charge on each capacitor is Q₀.

Now, formula for charge stored on a capacitor is;

Q = CV

Where;

Q is charge

C is capacitance

V is voltage

Thus, total charge stored on the two capacitors will be;

Q = Q₁ + Q₂

Since Q₀ is the charge on each capacitor, then;

For Capacitor 1, we have; Q₀ = C₁V

For capacitor 2, we have; Q₀ = C₂V

Thus, let the capacitance C₁ be be half the capacitance C of two capacitors.

Thus;

C₁ = ¹/₂C

Thus;

Q₀ =  ¹/₂CV

2Q₀ = CV

Now, a dielectric with dielectric constant k > 1 is inserted between the plates of capacitor C₁. Thus, the two capacitors will now be kC and C.

Thus;

C₂ = (kC × C)/(kC + C)

C will cancel out to give;

C₂ = kC/(k + 1)

Earlier on, we saw that;

Q₀ = C₂V

Thus;

Q₀ = kCV/(k + 1)

Earlier, we saw that 2Q₀ = CV

Thus, charge is;

Q₀ = 2kQ₀/(k + 1)

Since 2 capacitors, then total positive charge stored is;

2 × 2kQ₀/(k + 1) = 4kQ₀/(k + 1)

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The unstretched length of the spring is 32.67 m.

Spring Constant = k = 1.44 N/m

Weight of the apple = m = 1.2 N

Acceleration due to gravity = g = 9.8 m/s²

Length of unstretched spring = I

Frequency of SHM motion is given by ;

= f = (1/2π) √(k/m)

Frequency of pendulum is given by;

= f' = (1/2π) √(g/l)

In the question, f' =2f, thus,

= (1/2π) √(g/l) = 2 X (1/2π) √(k/m)

= √(g/l) = (1/2) √(k/m)

Squaring on both sides,

= g/l = k/4m

= l = (g X 4m ) / k

= l = ( 9.8 X 1.2 X 4 ) / 1.44

= l =  32.67 m

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The complete question:

An apple weighs 1.00 N. When you hang it from the end of a long spring of force constant 1.50 N/m and negligible mass, it bounces up and down in SHM. If you stop the bouncing and let the apple swing from side to side through a small angle, the frequency of this simple pendulum is half the bounce frequency. (Because the angle is small, the back-andforth swings do not cause any appreciable change in the length of the spring.) What is the unstretched length of the spring (with the apple removed)?

The plane of a loop of wire is perpendicular to a magnetic field. Rank, from greatest to least, the magnitudes of the loop's induced emf for each situation will be E - B - D - A-C.

Magnetic field strength is one of two ways that the intensity of a magnetic field can be expressed. Technically, a distinction is made between magnetic field strength H, measured in amperes per meter, and magnetic flux density B, measured in Newton-meters per ampere, also called tesla.

A current I through a long, straight wire produces a magnetic field with strength H=I/2πr at a distance r from the wire. So the field strength is inversely proportional to the distance from the wire.

The unit of magnetic field strength happens to be ampere per meter or A/m. Furthermore, the symbol of the magnetic field strength happens to be H.

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The absolute significance of a star is 10 parsecs distance , M is the significance the big name could have if it become located at a distance of 10 parsecs from Earth.

By thinking about stars at a set distance, astronomers can evaluate the real (intrinsic) brightnesses of various stars.Apparent significance is the brightness of a celebrity because it seems to the observer. This is what stargazers look at after they study the sky and spot that a few stars are brighter than others. Absolute significance is the brightness of a celebrity from a distance of 10 parsecs away. A parsec is same to 32.6 light-years.

Astronomers outline big name brightness in phrases of obvious significance — how shiny the big name seems from Earth — and absolute significance — how shiny the big name seems at a popular distance of 32.6 light-years, or 10 parsecs.

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You are required to gauge a crank shaft's rotational speed. The device's level of uncertainty will be 0%.

The number of rotations a rotating system completes in a predetermined amount of time is the measure of rotational speed, also known as speed or speed of rotation. Pump speed is often expressed in min-1, while rotational speed is measured in s-1 (rev/s) (rpm).

The term "angular velocity" or "rotational velocity" ( or ), also known as "angular frequency vector," refers to a pseudovector that expresses how quickly an item spins or circles in relation to a point or axis or changes its angular location or orientation over time.

The velocity meter's resolution = 2 rpm.

accuracy = 1.5%.

40 rpm = 1.5%.

The speed can change at 40 rpm = 39.7 to 40.3 rpm.

The device's resolution = 2 rpm.

uncertainty = 0%.

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Expression for the potential energy is (3/4)x⁴ - 2x² + x.

Potential energy is the energy possessed by the system when it is in rest.

If the potential energy function U(x) is known, then the force F(x) at any position can be obtained by the derivative of the potential.

F(x) = - dU/dx

dU = - F(x).dx

U = [tex]\int\{F(x)} \, dx[/tex]

U = [tex]\int[/tex](1 - 4x + 4x³) .dx

U = (3/4)x⁴ - 2x² + x

Plotting F(x) between x=-2 to x=+2,

F(x) = (1 - 4x + 4x³)

for x=-2, F(-2) = F{1 - 4(-2) + 4(-2)³}

F(-2) = {1 + 8 - 32}

F(-2) = (-23)

for x=+2, F(-2) = F{1 - 4(2) + 4(2)³}

F(2) = {1 - 8 + 32}

F(2) = 25

Plotting U(x) between x=-2 to x=+2

U(x) = (3/4)x⁴ - 2x² + x

for x=-2, U(-2) = {(3/4)(-2)⁴ - 2(-2)² + (-2)}

U(-2) = {(4*3) - (2*4) - 2}

U(-2) = 12 - 8 - 2  

U(-2) = 2

for x=2, U(2) = {(3/4)(2)⁴ - 2(2)² + (2)}

U(2) = {(4*3) - (2*4) + 2}

U(2) = {12 - 8 + 2}

U(2) = 6

For equilibrium points, force must be equal to zero,

F(x) = 0

(1 - 4x + 4x³) = 0

x1 = -1.10716

x2 = 0.26959

x3 = 0.83757

Equilibrium points exists at points x1, x2, x3.

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The speed of the ball at the bottom of the circle when ball of mass m, at one end of a string of length L, rotates in a vertical circle is √Lg

The rate at which an object's distance traveled changes is measured by its speed. In terms of measurement, speed is a scalar, meaning it has magnitude but no direction. Speed is the rate at which an object moves over a given distance. a thing that travels at a high rate of speed and covers a lot of distance quickly. A slow-moving object, on the other hand, travels a comparatively short distance in the same amount of time when moving at a low speed. An object with zero speed is completely immobile.

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The frequency of rotation of an object revolving around an axis is sometimes referred to as the rotational speed or rate of rotation of the object. Cycles per second (cps), revolutions per minute (rpm), etc. are some examples of its unit (the Greek lowercase letter nu).

What is the rotational frequency formula?

By a factor of 2, angular frequency (measured in radians per second) is bigger than frequency (measured in cycles per second, commonly known as Hz). In this picture, frequency is represented by the symbol rather than f. a sphere that is revolving about an axis. In order to satisfy = v / r, points further from the axis move more quickly.

How can I determine frequency?

Divide the number of times the event happens over the period of time to determine the frequency. Example: Anna divides the time by the quantity of page clicks (236). (one hour, or 60 minutes). She discovers that her clickthrough rate is 3.9 per minute.

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A) 3.99 cm, B)-7.99 cm/s, C)-15 cm/s2, D) 4 cm, In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the following expression,

a) At t=0

x=4.00cm)cos(3t+π/6)(a)= 4*0.999 = 3.999 cm

b)Expression for velocity v = dx/dt = -8.00 Sin(3t+π/6)

At t=0 v= -8 Sin(π/6) =  -7.999 cm/s

c) Expression for acceleration a= -16 Cos(3t+ π/6)

At t=0 a= -16 Cos(π/6) = -15.99 cm/ sec2

d) Period = (2 ?)/3

  Amplitude= 4 cm

A piston is a part of a variety of comparable devices, including reciprocating engines, reciprocating pumps, gas compressors, hydraulic cylinders, and pneumatic cylinders.

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The waves for the boat of fisherman is travelling with the speed of 1.203 m/s and the amplitude of each wave is 0.35 m.

The rate at which a wave travels a certain distance in a given amount of time is referred to as its speed.

The boat travels 0.700 meters from its highest point to its lowest point. The boat requires 2.70 minutes to travel.

The fisherman notices that the wave crests are 6.50 meters apart horizontally. Since the wave's wavelength is determined by the horizontal spacing between crests. Consequently, the wave's wavelength is,

lambda=6.50s

The wave's period is equal to the time it takes to travel from its peak to lowest point. Consequently, the wave's period is,

T=2X2.7

T=5.4s

The relationship between wavelength and time period determines the wave's speed. Consequently, the waves' traveling speed is,

v=6.50/5.4

v=1.203m/s

The wave's amplitude is equal to half of the distance between its peak and lowest points.

The boat now travels 0.700 meters from its highest point to its lowest position. As a result, each wave's amplitude is A=0.7/2.A=0.35m.

As a result, the waves for the fishing boat are moving at a speed of 1.203 m/s and have an amplitude of 0.35 m.

Waves that are relatively tiny move at speeds of up to 10 km/h and touch the shore once every three seconds. Though they travel at a speed of over 50 km/h, very huge waves arrive less frequently—once every 14 seconds—because of their longer wavelengths.

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a) The number of hours it takes for the satellite to make one orbit ( h ) = 1.64 hours, b) The speed of the Aura spacecraft = 7.5 Km/s.

Height of satellite Orbit ( h ) = 705 km ≈ 705000 m

a) Determine the time taken in hours for the satellite to make a single orbit

T = 2π [tex]\sqrt{ (R + h)^{2} /GM[/tex]

G = 6.67 * 1011 N-m2/kg2, M (earth's mass) = 5.98 * 1024, R = 6.38 * 106 m, and h = 705000 m

Fill in the values for T = 5933 seconds to equal 1.64 hours ( time taken to complete one orbit )

B) Calculate the spaceship Aura's speed

V =  [tex]\sqrt{GM/R + h}[/tex]

G = 6.67 * 1011 N-m2/kg2, M (earth's mass) = 5.98 * 1024, R = 6.38 * 106 m, and h = 705000 m

Fill in the values in the equation ( 2 )

V equals 7503 m/s, or 7.5 km/s.

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The maximum constant speed at which the elevator with a mass 1500 Kg can be lifted is 0.12 m/s.

To determine the maximum constant speed at which an elevator can be lifted, we need to consider the power available from the lifting device, in this case an electric motor, and the mass of the elevator and its occupants. The power available from the motor is given as 18 kW, and the mass of the elevator and its occupants is given as 1500 kg.

The speed of an object being lifted is directly related to the power available from the lifting device and the mass of the object being lifted. The relationship between these variables is given by the equation Power = mass * acceleration * velocity. By rearranging this equation to solve for velocity, we can determine the maximum constant speed at which the elevator can be lifted.

In this case, the acceleration of the elevator is equal to the acceleration due to gravity, which is 9.81 m/s^2. Plugging in the values for the power, mass, and acceleration, we get a maximum constant speed of 0.12 m/s for the elevator. This means that the elevator can be lifted at a constant speed of 0.12 m/s, given the power available from the electric motor and the mass of the elevator and its occupants.

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The option (d) is correct-This is because, the rod in D has same length as the vibrating rod (unlabeled) so its more likely to get in resonance with that that's why it oscillates more vigorously.

What is oscillates  ?

In a complex mixture of chemical compounds that are reacting, a chemical oscillator is one in which the concentration of one or more components changes on a regular basis.

What is vibrating rod ?

A trustworthy point level sensor for high and low level indication or plugged chute detection is a vibrating rod, also known as a vibrating level switch. Bulk densities of as little as 1.25 lb/ft3 can be used for their use in light, fluffy powders and flakes.

Therefore, option (d) is correct-This is because, the rod in D has same length as the vibrating rod (unlabeled) so its more likely to get in resonance with that that's why it oscillates more vigorously.

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The magnetic flux through the small loop when the current through the solenoid is 2.50 A is 5.87*10⁻⁴ Wb, the induced emf in the loop is 1.4*10⁻³r.

What is magnetic flux  ?

The number of magnetic field lines that travel through a specific closed surface is referred to as magnetic flux. It gives a measurement of the overall magnetic field that traverses a specific surface region.

What is  induced emf  ?

A magnetic field is induced when a conductor carrying an electric current travels through it. Induced electromagnetic fields (EMFs) are created when a magnetic field rotates around an electric field.

Given data

length = 0.100 m

radius = 0.50 m

N= 1.5 *10⁴

I= 2.50A

a) the field inside the solenoid  is

B= μ₀ Ni/L

B= 1.25 *10⁻⁶*1.5*10⁴*2.50/0.100

B= 0.47 Tesla

B= 0.47 W₆/m²

Area, A= πr²= (0.02)²

=0.00125m²

Magnetic flux = ∅ = B.A

= 5.87*10⁻⁴ Wb

b) induced Emf in the loop

EMf =  μ₀ (dI/dT) (N/L) πr²

EMF= 1.4*10⁻³r

Therefore, the magnetic flux through the small loop when the current through the solenoid is 2.50 A is 5.87*10⁻⁴ Wb, the induced emf in the loop is 1.4*10⁻³r.

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The buoyancy force when measured on an object submerged in molasses instead of water the buoyancy force does not differ.

Buoyancy is the force that is applied by any fluid on the body which is submerged in it.

The buoyancy force on any body is given by the relation,

B = Vpg

Where,

V is the volume of the fluid displaced,

p is the density of the fluid,

g is the acceleration due to gravity.

If we assume that the object is floating on the surface of the fluid then the buoyancy force will be equal to the weight of the body.

So, if the buoyancy force is measured on molasses instead of water the boils force will not differ in magnitude because it will be equal to the weight of the body in both the cases.

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The heat released during the process of applying the break of the car is 200000 Joules.

According to the law of conservation of energy, energy can nether be created nor be destroyed, it can only be converted from one form to another.

In the process when the brakes of the car are applied the kinetic energy of the car is changing from 300000 to 100000 Joules.

When the kinetic energy of the body is getting converted into the thermal energy because of the friction the loss of kinetic energy is taking place.

It has to be noted here that the law of conservation of energy is still valid because all the energy that is lost in the form of thermal energy has gone into the environment which is ultimately a bigger system and the energy is still constant for the universe.

So, the amount of energy that is lost is 200000 Joules.

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