Ultrasound is the name given to frequencies above the human range of hearing True or false

The energy required to raise the temperature of Lake Erie's water from 17.8°C to 21.6°C is 1.96×10¹⁶ J. It would take approximately 4.11×10^9 years to supply this amount of energy using a 1,400-MW exhaust energy of an electric power plant.

To calculate the energy required to raise the temperature of Lake Erie's water from 17.8°C to 21.6°C, we need to use the formula Q = mcΔT, where Q is the energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Given that Lake Erie contains 4.00 ✕ 10^11 m³ of water and assuming the density of water at 20°C and 1 atm to calculate mass, we can find the energy. Using the formula, Q = mcΔT, we can substitute the values and calculate the energy as 1.96×10¹⁶ J.

For part (b), we need to determine how many years it would take to supply this amount of energy using a 1,400-MW exhaust energy of an electric power plant. The formula to calculate the energy supplied by the power plant over a certain time period is E = Pt, where E is the energy, P is the power, and t is the time. Rearranging the formula to solve for time, t = E/P, we can substitute the values and calculate the time as approximately 4.11×10^9 years.

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The student's question requires us to use the equation for heat change to calculate the energy needed to raise the temperature of Lake Erie by a few degrees. We also need to calculate the time it would take for a power plant to produce this amount of energy. The answers we found are approximately 6.36 × 10^24 joules and 1.44 × 10^8 years respectively.

To answer the student's question, we first need to calculate the energy required to raise the temperature of Lake Erie from 17.8°C to 21.6°C. The formula for this calculation involves the specific heat of water, the mass of the water, and the change in temperature. Specifically:

ΔQ = m × c × ΔT

where m is the mass of the water, c is the specific heat of water (4.184 J/g°C), and ΔT is the temperature change (21.6°C - 17.8°C = 3.8°C). Since the volume of Lake Erie is given as 4.00 × 10^11 m³ and we're assuming the density of water is about 1 g/cm³, we multiply the volume by the density to get approximately 4.00 × 10^20 g. Our calculation then becomes:

ΔQ = (4.00 × 10^20 g) × (4.184 J/g°C) × (3.8°C) = approximately 6.36 × 10^24 J.

To answer the second part of the question, we need to convert the power of the power plant from MW to J/s. 1 MW is equivalent to 1 × 10^6 J/s, so the plant is producing 1.4 × 10^9 J/s. To find out how long it would take to produce the energy calculated in the first part, we simply divide the total energy requirement by the energy production rate of the power plant, which gives us:

Time = (6.36 × 10^24 J) / (1.4 × 10^9 J/s) = approximately 4.54 × 10^15 seconds. Converting seconds to years, we get approximately 1.44 × 10^8 years.

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1. -23.2 J

The gravitational potential energy of the ball is given by

[tex]U=mgh[/tex]

where

m = 1.1 kg is the mass of the ball

g = 9.8 m/s^2 is the acceleration of gravity

h is the height of the ball, relative to the reference point chosen

In this part of the problem, the reference point is the ceiling. So, the ball is located 2.16 m below the ceiling: therefore, the heigth is

h = -2.16 m

And the gravitational potential energy is

[tex]U=(1.1 kg)(9.8 m/s^2)(-2.16 m)=-23.2 J[/tex]

2. 41.1 J

Again, the gravitational potential energy of the ball is given by

[tex]U=mgh[/tex]

In this part of the problem, the reference point is the floor.

The height of the ball relative to the floor is equal to the height of the floor minus the length of the string:

h = 5.97 m - 2.16 m = 3.81 m

And so the gravitational potential energy of the ball relative to the floor is

[tex]U=(1.1 kg)(9.8 m/s^2)(3.81 m)=41.1 J[/tex]

3. 0 J

As before, the gravitational potential energy of the ball is given by

[tex]U=mgh[/tex]

Here the reference point is a point at the same elevation of the ball.

This means that the heigth of the ball relative to that point is zero:

h = 0 m

And so the gravitational potential energy is

[tex]U=(1.1 kg)(9.8 m/s^2)(0 m)=0 J[/tex]

Answer:

A. weight of air it displaces.

Explanation:

The force that buoys up a balloon is equal to the weight of the air it displaces, as per Archimedes' Principle.

The force that buoys up a balloon is equal to the weight of the air it displaces. This principle is known as Archimedes' principle and it applies to both liquids and gases, like air. According to this principle, the upward buoyant force exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.

In the context of a balloon floating in the air, the balloon and the gas inside it displace a volume of air. The weight of this displaced air pushes upward on the balloon, providing the buoyant force. If the weight of the balloon and the gas inside it are less than the weight of the displaced air, the balloon will rise up into the atmosphere.

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Answer:

A) The electric and magnetic fields must be perpendicular to each other in that region

Explanation:

The proton does not experience any acceleration: this means that the net force acting on it is zero.

Therefore, this also means that the electric force and the magnetic force acting on the proton are balanced.

Let's remind that:

- The electric force acting on a positive charged particle has the same direction as the electric field:

F=qE

where F is the force, q is the charge, E is the electric field

- The magnetic force acting on a positive charged particle in motion is perpendicular to the direction of the magnetic field:

F=qv ∧ B

where q is the charge, v is the velocity of the particle, B is the magnetic field

Therefore, for the two forces to be along the same line (but in opposite directions), we must have that the electric field E and the magnetic field B are perpendicular to each other.

The correct statement is that the magnetic field must be zero but not the electric field for a proton moving without acceleration in a region of space, as only then will it not be deflected from its path.

The correct answer to the student's question is E) The magnetic field must be zero but not the electric field in that region. This can be understood by examining the forces experienced by a moving charged particle such as a proton in an electric field and magnetic field. A charged particle moving in a magnetic field experiences a Lorentz force that is always perpendicular to both the particle's velocity and the magnetic field direction.

If the proton is not accelerating in the direction of motion, it implies there's no net force acting on it in that direction. Since a magnetic field's force would always cause an acceleration perpendicular to the velocity, for a proton moving in a straight line with no acceleration, the magnetic field must be zero or parallel to the movement direction.

However, an electric field, if present, could be exerting a force on the proton balanced exactly by other forces (such as another opposite electric field), allowing the proton to have zero net force and continue its motion unaccelerated. Hence, a non-zero electric field could exist, but the magnetic field must be zero or not exerting any influence causing perpendicular acceleration of the proton.

Answer:

Coefficient of static friction is normally greater than coefficient of sliding friction which is also known as coefficient of kinetic friction.

Explanation:

Coefficient of friction can be seen as the cumulative effect of the irregularities that are on the surface of objects. When these interlocking get locked into one another a resistance arises to the motion of the object which is termed as friction. When an object is static these irregularities get more time to be interlocked as compared to when an object is in motion thus the coefficient of static friction is more than the coefficient of sliding friction.

Static friction is normally greater than sliding friction on the same object because it takes more force to start an object moving than to keep it moving.

In general, static friction is normally greater than sliding friction on the same object. Static friction occurs when two surfaces are in contact but not moving relative to each other, while sliding friction occurs when two surfaces are sliding past each other.

The force of static friction is needed to prevent the object from moving, and it can be greater than the force of sliding friction because it takes more force to start an object moving than to keep it moving. This is why it is often harder to start sliding a heavy object compared to keeping it sliding.

For example, imagine trying to push a heavy box on the ground. Initially, you need to apply a greater force to overcome the static friction and start the box moving. Once the box is sliding, the force required to keep it sliding (sliding friction) is usually less than the force needed to start it moving (static friction).

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Answer: lambda [tex]\lambda[/tex], nu [tex]\nu[/tex], and 100E

Explanation:

The energy [tex]E[/tex] of a photon is given by:

[tex]E=h\nu[/tex]   (1)

Where:

[tex]h[/tex] is the Planck constant

[tex]nu[/tex] is the frequency

On the other hand, we have an expression that relates the frequency of the photn with its wavelength [tex]\lambda[/tex]:

[tex]nu=\frac{c}{\lambda}[/tex] (2) where [tex]c[/tex] is the speed of light

Substituting (2) in (1):

[tex]E=h\frac{c}{\lambda}[/tex]   (3) This is the energy for a single photon

For 100 photons, the energy is:

[tex]100E=100(h\frac{c}{\lambda})=100h\nu[/tex]   (3)

Where the wavelength and the frequency of the light remains constant.

Therefore, the answer is:

[tex]\lambda[/tex], [tex]\nu[/tex], and 100E

The wavelength, frequency, and energy of a pulse of light containing 100 of these photons is a wavelength, a frequency and 100 energy. Therefore the correct  answer is E.

1. The wavelength [tex](\(\lambda\))[/tex] and frequency (nu) of a photon are related by the speed of light ([tex]\(c\)[/tex]) in a vacuum: [tex]\(c = \lambda \nu\)[/tex].

2. The energy (E) of a photon is related to its frequency by Planck's equation: [tex]\(E = h \nu\)[/tex], where (h) is Planck's constant.

3. For a pulse of light containing 100 photons, the total energy is the sum of the energies of the individual photons.

4. Therefore, the pulse would have the same wavelength ([tex]\(\lambda\)[/tex]), the same frequency [tex](\(\nu\)),[/tex] and 100 times the energy [tex](\(100E\))[/tex] compared to a single photon.

Thus, the correct choice is option E. [tex]\(\lambda, \nu, \text{ and } 100E\)[/tex].

Complete question:

Consider a single photon with a wavelength [tex]\(\lambda\)[/tex], a frequency (nu), and an energy (E). What is the wavelength, frequency, and energy of a pulse of light containing 100 of these photons?

A. [tex]\(0.01 \lambda, \nu, \text{ and } 100E\)[/tex]

B. [tex]\(0.01 \lambda, 0.01 \nu, \text{ and } 0.01 E\)[/tex]

C. [tex]\(100 \lambda, 100 \nu, \text{ and } E\)[/tex]

D. [tex]\(100 \lambda, 100 \nu, \text{ and } 100 E\)[/tex]

E. [tex]\(\lambda, \nu, \text{ and } 100E\)[/tex]

Answer:

[tex]v_1 = 12 volts[/tex]

[tex]v_2 = 6 volts[/tex]

[tex]v_3 = 36 volts[/tex]

Explanation:

As we know that all the batteries are in series

so the net voltage of all three batteries is given as

[tex]V = v_1 + v_2 + v_3[/tex]

now we know that

[tex]v_1 = 2v_2[/tex]

[tex]v_1 = \frac{1}{3}v_3[/tex]

now plug in all the values in it

[tex]54 = v_1 + \frac{v_1}{2} + 3v_1[/tex]

[tex]54 = 4.5 v_1[/tex]

[tex]v_1 = 12 volts[/tex]

now we have

[tex]v_2 = 6 volts[/tex]

[tex]v_3 = 36 volts[/tex]

Final answer:

To find the actual voltage of each battery connected in series to get a total of 54 volts, we can assign variables to represent the voltage of each battery. By using the given information, we can set up and solve an equation to find the values of the variables.

Explanation:

To find the actual voltage of each battery, we'll assign variables to each battery's voltage. Let's say the voltage of the second battery is x volts.

Using the information given, we know that the voltage of the first battery is twice the voltage of the second battery, so it is 2x volts. The voltage of the third battery is 1/3 the voltage of the first battery, so it is (1/3)(2x) = 2x/3 volts.

Since the total voltage when the batteries are connected in series is 54 volts, we can write the equation: 2x + x + 2x/3 = 54. Solving this equation, we find that x = 15 volts. Therefore, the voltage of the first battery is 2x volts = 2(15) = 30 volts, the voltage of the second battery is x volts = 15 volts, and the voltage of the third battery is 2x/3 volts = (2/3)(15) = 10 volts.

Answer:

There is no way by which we can tell weather we are on the earth or we left the earth.

Explanation:

Our body responses to acceleration alone when we accelerate upwards at [tex]9.8m/s^{2}[/tex] a fictitious force equal to our [tex]mass\times acceleration[/tex] acts on our body which in this case of acceleration is same as our weight thus we will still feel the effect of gravity thus cannot say weather we left earth or are still there.

Final answer:

To find the mass of the baseball, we can use the concept of impulse, which is equal to the change in momentum. We are given the net eastward impulse delivered by the bat and the initial and final velocities of the baseball. By using the equation for impulse, we can calculate the mass of the baseball to be 170 grams.

Explanation:

To find the mass of the baseball, we can use the concept of impulse. Impulse is equal to the change in momentum, which is the product of mass and velocity. In this case, we are given the net eastward impulse delivered by the bat (1.5 N-s) and the initial and final velocities of the baseball (-3.8 m/s and 4.9 m/s, respectively).

Since the impulse is equal to the change in momentum, we can write the equation:

Impulse = (mass of the baseball)(final velocity - initial velocity)

Substituting the given values, we have:

1.5 = (mass of the baseball)(4.9 - (-3.8))

Simplifying the equation and solving for the mass of the baseball:

mass of the baseball = 1.5 / (4.9 - (-3.8))

mass of the baseball = 1.5 / 8.7

mass of the baseball = 0.17 kg

However, the question asks for the mass of the baseball in grams. Therefore, we need to convert the mass from kilograms to grams:

mass of the baseball = 0.17 kg * 1000 g/kg

mass of the baseball = 170 g

Answer:

option (c)

Explanation:

If a large force is applied on an object for a small duration of time, it is called impulsive force. for example, a bat's man hit the ball. here the contact time of bat and ball is very small while the force applied by the bat is very large.

Impulse = force x small time

To decrease the impulsive effect, the time should be increased.

Catching a fast-moving softball by extending the hand and reducing the force involves increasing the time of the catch, which decreases acceleration and the force needed to stop the ball.

The correct answer to the question is c. time of catch is increased. When catching a fast-moving softball, extending the hand forward just before the catch and allowing the ball to ride backward with the hand effectively increases the time over which the ball is decelerated to a stop. This is due to Newton's second law, which states that the force exerted on an object is equal to the mass of the object times its acceleration (F=ma). By increasing the time of the catch, the acceleration is decreased, and thus the force experienced by the hand is also reduced. This is in contrast to catching the ball abruptly, which would result in a short catch time, higher acceleration, and therefore a larger force needed to stop the ball.

(a) 44.7 m/s

We can find the final velocity of the car by using the SUVAT equation:

[tex]v^2-u^2 = 2ad[/tex]

where

v is the final velocity

u = 0 is the initial velocity (the car starts from rest)

[tex]a=0.5 m/s^2[/tex] is the acceleration

[tex]d=2km = 2000 m[/tex] is the displacement

Solving for v,

[tex]v=\sqrt{u^2 +2ad}=\sqrt{0+2(0.5)(2000)}=44.7 m/s[/tex]

(b) 80 s

We can find the time it takes for the car to cover 1.6 km by using the following SUVAT equation:

[tex]d=ut+\frac{1}{2}at^2[/tex]

where in this case we have

d = 1.6 km = 1600 m is the displacement

[tex]a=0.5 m/s^2[/tex] is the acceleration

u = 0

t is the time

Solving for t, we find:

[tex]t=\sqrt{\frac{2d}{a}}=\sqrt{\frac{2(1600)}{0.5}}=80 s[/tex]

Answer:E=[tex]\frac{\pi R\left ( \Delta V\right )^2\sqrt{LC}}{\left ( R^2+\frac{9}{4}\left (\frac{L}{C} \right )\right )}[/tex]

Explanation:

We know resonant frequency is given by

[tex]\omega_0=\frac{1}{\sqrt{LC}}[/tex]

and the operating frequency is given by

[tex]\omega =2\omega_0=\frac{2}{\sqrt{LC}}[/tex]

The capacitance reactance is given by

[tex]X_c=\frac{1}{\omega C}=\frac{\sqrt{LC}}{2C}=\frac{1}{2}\sqrt{\frac{L}{C}}[/tex]

inductive reactance is given by

[tex]X_L=\omega L=\left ( \frac{2}{\sqrt{LC}}\right )L=2\sqrt{\frac{L}{C}}[/tex]

Thus impedance is

[tex]Z=\left ( R^2+\left (X_L-X_C \right )^2 \right )^\frac{1}{2}[/tex]

[tex]Z=\left ( R^2+\left (2\sqrt{\frac{L}{C}}-\frac{1}{2}\sqrt{\frac{L}{C}} \right )^2 \right )^\frac{1}{2}[/tex]

[tex]Z=\left ( R^2+\frac{9}{4}\left ( \frac{L}{C} \right ) \right )^\frac{1}{2}[/tex]

The average power delivered is

[tex]P_{avg.}=\frac{\Delta V^2}{Z}cos\phi =\frac{\left ( \Delta V\right )^2}{Z}\left (\frac{R}{Z} \right )[/tex]

[tex]P_{avg.}=\frac{\left (\Delta V \right )^2R}{\left ( R^2+\frac{9}{4}\left (\frac{L}{C} \right )\right )}[/tex]

Energy Delivered in one cycle is given by

[tex]E=P_{avg}T[/tex]

[tex]E=\frac{\left (\Delta V \right )^2R}{\left ( R^2+\frac{9}{4}\left (\frac{L}{C} \right )\right )}\left ( \frac{2\pi }{\frac{2}{\sqrt{LC}}}\right )[/tex]

E=[tex]\frac{\pi R\left ( \Delta V\right )^2\sqrt{LC}}{\left ( R^2+\frac{9}{4}\left (\frac{L}{C} \right )\right )}[/tex]              

Heat flows from the hot to cold substance.

Answer: Option A

Explanation:

The medium or substance which has the higher temperature referred to as the hot substance transmits heat to the less temperature body or substance referred to as the cold substance. The temperature difference makes the heat flow from warmer substance to cooler substance.

The temperature thus flows through the gradient from high to low. This transmission takes place until both the substance in contact becomes equal in temperature.

Answer:

The answer is D

Hope this helps!!

Answer: D. Performing a fair test in which only the independent variable affects the dependent variable.

Explanation:

Validity is a measure of how correct the result of the experiment is. The validity of the experiment is based upon the correctness of the research topic, and correctness and implementation of the scientific procedures.  

Performing a fair test that can be based upon use of the independent and dependent variables can yield results which will be valid and acceptable. The independent variable in an experiment is the variable which can be changed to know it's affect on the dependent variable. The dependent variable will help in determining the result of the experiment.

Answer:

option (c)

Explanation:

The time taken by the pendulum to complete one oscillation is called time period.

The number of oscillations completed in one second is called frequency.

The frequency is the reciprocal of time period.

T = 1 / f

If the period is doubled, then the frequency is halved.

Answer:

A) 100°C

B) 211 g

Explanation:

Heat released by red hot iron to cool to 100°C = 130 x .45 x 645 [ specific heat of iron is .45 J /g/K]

= 37732.5 J

heat required by water to heat up to 100 °C = 85 x 4.2 x 80 = 28560 J

As this heat is less than the heat supplied by iron so equilibrium temperature will be 100 ° C. Let m g of water is vaporized in the process . Heat required for vaporization = m x 540x4.2  = 2268m J

Heat required to warm the water of 85 g to 100 °C = 85X4.2 X 80 = 28560 J

heat lost = heat gained

37732.5 = 28560 + 2268m

m = 4 g.

So  4 g of water will be vaporized and remaining 81 g of water and 130 g of iron that is total of 211 g will be in the cup . final temp of water will be 100 °C.

The final temperature of the water is 100°C

The final mass of the iron and the remaining water is 211 g

The heat released by red hot iron to cool to 100°C

= 130 x .45 x 645 [ specific heat of iron is .45 J /g/K]

= 37732.5 J

The heat required by water to heat up to 100 °C

= 85 x 4.2 x 80

= 28560 J

As this heat is less than the heat supplied by iron, the equilibrium temperature will be 100 ° C. Let mg of water that is vaporized in the process is

Heat required for vaporization

= m x 540x4.2  

= 2268m J

The heat required to warm the water of 85 g to 100 °C

= 85X4.2 X 80

= 28560 J

heat lost = heat gained

37732.5

= 28560 + 2268m

m = 4 g.

So, 4 g of water will be vaporized, and the remaining 81 g of water and 130 g of iron which is a total of 211 g will be in the cup .

The final temp of the water will be 100 °C.

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Answer:

The heat of vaporization 580 cal/g times 602g = cal in human  and do the same for life form.

Explanation:

Answer:

Increased.

Explanation:

Given that in 200 mL of the beaker contains saturated solution of KI.

Whenever we allow the solution to heat or to evaporate, only water present in the solution evaporates because it is volatile while the salt is non volatile and thus do not evaporate.

When we decrease the volume of water in the beaker to 100 mL, the concentration of the salt, KI in the solution increases as the same amount of the salt is present in less amount of volume of the solvent.

Answer:

reduced speed comes out to be 48.3 km/hr

Explanation:

intial speed = 65 miles per hour

final speed = 35 miles per hour

reduced speed = initial speed - final speed

                          =  65  - 35

                          =  30 mile/hr

1 km = 0.62 mile

1 miles =  1.61 km/hr

so reduce speed in (km/hr) = 30 ×1.61 km/hr

                                             =  48.3 km/hr

hence the reduced speed comes out to be 48.3 km/hr

Answer:

2412 psi is the pressure of the gas mixture in the tank.

Explanation:

Pressure of the helium gas = 1,906 psi

Volume of the helium gas = 7.25 L

Pressure of the oxygen gas = 506 psi

Volume of the oxygen gas = 7.25 L

After mixing both gases in a container with volume 7.25 L at with constant temperature.

Since, the temperature and volume remained constant, pressure becomes directly dependent on moles of gases.So, when we mix gases together the moles of gases will also add and along with that pressure of individual gas will also get added to give total pressure of the mixture in a tank.

Total pressure = pressure(Heluim)+pressure(oxygen)

[tex]P_{total}=1,906 psi+506 psi=2,412 psi[/tex]

2412 psi is the pressure of the gas mixture in the tank.

Answer: The following statement is true about squall line thunderstorm development: These often form ahead of the advancing front but rarely behind it because lifting of warm, humid air and the generation of a squall line usually occur in the warm sector ahead of an advancing cold front. Behind a cold front, the air motions are usually downward, and the air is cooler and drier.

An upper-level wave, accountable for the fabrication of a squall line, extend in front of and backside a cold front, the air backside the front is cold, steady and settling while the air ahead of the front is hot and co-seismic.

Final answer:

Squall lines often form ahead of advancing fronts due to warm, humid air lifting, while behind a cold front, the air is cooler and drier.

Explanation:

The statement is true concerning squall line thunderstorm development. Squall lines typically form ahead of an advancing front due to the lifting of warm, humid air in the warm sector ahead of an advancing cold front. Behind a cold front, the air motions are usually downward, and the air is cooler and drier.

When you take US appliances to Europe, or any of the many other places in the world where the 'mains' outlets supply 240 volts, you can't just plug your device into the 240 volts.  It'll overheat, smoke, and die if you do.  

You need some kind of a power "converter", that will change the 240V to the 120V that your device recognizes from back home, and is designed to work with.

If your device uses more than just a few watts of power to operate, then you'll need a converter that's based on a transformer.  It'll be heavy and pretty bulky, but that's what it takes to do the job.

The transformer is a "step-down" unit. You put 240 volts into it, it steps that down, and 120 volts comes out of it.  

To use a hair blower designed for a 120V supply in a region with a 240V supply, you need a step-down voltage converter, which reduces the voltage to a level that the device can handle.

To operate a hair blower designed for 120V in a region which provides 240V, you need to use a device known as a voltage converter or power converter. As you want to reduce the voltage from 240V to 120V, you would need a step-down converter.

The converter works by reducing the voltage offered by the power source (in this case, 240V) to a level the device can handle (120V). Without such a converter, plugging the hair blower in directly would likely cause it to be ruined, as it isn't constructed to handle such a high voltage.

It’s also important to remember that different regions have different power plug formats, so you may also need to carry a plug adapter.

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Electrostatic force between two points in space is defined as,

[tex]F_e=\dfrac{Q_1Q_2}{4\pi r\epsilon_r\epsilon_0}[/tex]

The r is the distance between them.

So if,

[tex]1N=\dfrac{Q_1Q_2}{4\pi 2cm\epsilon_r\epsilon_0}\Rightarrow 2\cdot1N=\dfrac{Q_1Q_2}{4\pi\cdot10^{-2}m\cdot\epsilon_r\epsilon_0}[/tex]

Than,

[tex]\boxed{\dfrac{1}{4}N}=\dfrac{Q_1Q_2}{4\pi\cdot 8cm\cdot\epsilon_r\epsilon_0}\Rightarrow8\dfrac{1}{4}N\Leftrightarrow 2N=\dfrac{Q_1Q_2}{4\pi\cdot10^{-2}m\cdot\epsilon_r\epsilon_0}[/tex]

Hope this helps.

r3t40

Answer:

2144 rad/s

Explanation:

R1 = R

ω1 = 536 rad/s

R2 = R/2

ω2 = ?

Mass is M

By use of angular momentum remains constant if no external force is acting on the body.

I1 ω1 = I2 ω2

The moment of inertia of solid sphere is 12/5 MR^2

So, 2/5 x M R^2 x 536 = 2/5 x M (R/2)^2 x ω2

536 = ω2 / 4

ω2 = 2144 rad/s

Answer:

ω₂ = 2144 rad/s

Explanation:

angular  speed =  536 radians/second

as, we all know the moment of inertia of solid sphere

[tex]I_{sphere}= \dfrac{2}{5}MR^2[/tex]

here in the question two radius are given

by using angular momentum conservation

[tex]I_1 \omega_1 = I_2 \omega_2[/tex]

[tex]\dfrac{2}{5}MR_1^2 \omega_1 =\dfrac{2}{5}MR_2^2 \omega_2\\R^2\times 536= \dfrac{R^2}{4}\times \omega_2[/tex]

[tex]\omega_2 = 4 \times 536[/tex]

ω₂ = 2144 rad/s

Answer:

1. 3.8 m/s²

2. 2400 m/s

Explanation:

1. Acceleration due to gravity can be found with Newton's law of gravitation:

g = GM / R²

where g is the acceleration at the surface,

G is the universal gravitational constant,

M is the mass of the planet,

and R is the radius of the planet.

If we say M is the mass of the Earth and R is the radius of the Earth, then we know:

9.8 = GM / R²

Mars has a mass of 0.11 M and a radius of (4200/7900) R = 0.53 R.  So the acceleration is:

g = G (0.11 M) / (0.53 R)²

g = 0.39 GM / R²

g = 0.39 (9.8)

g = 3.8

So the value of g on Mars is 3.8 m/s².

2. The escape velocity is the velocity at which the kinetic energy of an object at the surface equals its gravitational potential energy.

½ m v² = m (GM / r²) r

½ v² = GM / r

v² = 2GM / r

v = √(2GM / r)

The mass of the moon is 7.35×10²² kg, and the radius of the moon is 1.74×10⁶ m.

v = √(2 (6.67×10⁻¹¹) (7.35×10²²) / (1.74×10⁶))

v = 2400 m/s

Answer: yes that is true

Explanation:

Answer:

[tex]\omega_f=0.0356 rev/day[/tex]

Explanation:

Given:

Angular speed [tex]\omega_1=2\ rev/day[/tex]

Radius of the solid sphere = R

Radius of the spherical shell, R' = 5.8R

now the initial moment of inertia i.e the moment of inertia of the solid sphere is given as:

[tex]I_i=\frac{2}{5}MR^2[/tex]

where, M is the mass of the solid sphere

Now, the final moment of inertia i.e the moment of inertia of the spherical shell is given as:

[tex]I_f=\frac{2}{3}MR'^2[/tex]

or

[tex]I_f=\frac{2}{3}M(5.8R)^2[/tex]

or

[tex]I_f=22.426MR^2[/tex]

Now applying the concept of conservation of angular momentum

we get

[tex]I_i\omega_i=I_f\omega_f[/tex]

substituting the values, we get

[tex]\frac{2}{5}MR^2\times 2=22.426\times MR^2\omega_f[/tex]

or

[tex]\omega_f=\frac{\frac{2}{5}\times 2}{22.426}=0.0356 rev/day[/tex]

[tex]f_{0}=159.2KHz[/tex]

In order to solve this problem we have to use the resonance frecuency equation [tex]f_{0}=\frac{1}{2\pi \sqrt{LC}}[/tex], at this frecuency in a LC circuit the capacitor and the inductor have the same reactance. So:

With C = 1.0μF and L = 1.0μH

[tex]f_{0}=\frac{1}{2\pi \sqrt{(1.0x10^{-6}F)(1.0x10^{-6}H)}}\\f_{0}=159155Hz\\f_{0}=159.2KHz[/tex]

The 1.0 μf capacitor and a 1.0 μh inductor have the same reactance at [tex]f_{0}[/tex] = 159.15 KHz.

A capacitor is a device that stores electrical energy.

An inductor is a device that stores electrical energy in the form of magnetic field.

Now, putting value of capacitor C and inductor L in above equation we get,

                                 [tex]f_{0}[/tex] = [tex]\frac{1}{2\pi \sqrt{LC} }[/tex]  

                                 [tex]f_{0}[/tex] = [tex]\frac{1}{2\pi \sqrt{(1.0x10^{-6})(1.0x10^{-6}) } }[/tex]

                                 [tex]f_{0}[/tex] = 159155 Hz.

Thus, for same reactance the frequency will be 159.2 KHz.

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Answer:

12.5 ft/s

Explanation:

Height of person = 6 ft

height of lamp post = 10 ft

According to the question,

dx / dt = 5 ft/s

Let the rate of tip of the shadow moves away is dy/dt.

According to the diagram

10 / y = 6 / (y - x)

10 y - 10 x = 6 y

y = 2.5 x

Differentiate both sides with respect to t.

dy / dt = 2.5 dx / dt

dy / dt = 2.5 (5) = 12.5 ft /s

When the person is 15 ft away from the pole, the rate is 7.5 ft/s.

The resultant displacement is calculated as follows;

[tex]R^2 = 6^2 + 10^2\\\\R = 11.6[/tex]

10 ft ------ 5 ft

15 ft ------- ?

= (15 x 5)/10

= 7.5 ft/s

Thus, when the person is 15 ft away from the pole, the rate is 7.5 ft/s.

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Answer:0.0242 Nm

Explanation: The distance of 0.145 mm is very small. This will also result in a small ttorque. The question would make more sense if the distance was 0.145 m. Answering with the 0.145 mm as distance :

Changin from mm to m : 1mm=0.001m

0.145 mm = 0.000145 m

The formula for Torque is T=Fxd

Wher F is the force and d is the perpendicular distance between the centre of the bolt and the applied force.

T= 167 x 0.000145 = 0.024215 Nm

The angular momentum quantum number can be any integer from 0 to n-1, describing the shape of the electron's orbital and the level of its angular momentum.

The angular momentum quantum number (l) can have any integer value from 0 to n-1, where n is the principal quantum number. This quantum number describes the shape of the electron's orbital, and it essentially tells us about the amount of angular momentum a subshell has. For instance, if the principal quantum number (n) is 3, l can be 0, 1, or 2, corresponding respectively to the s, p, and d orbitals.

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