The odometer of a car indicates the total distance travelled by the vehicle. A driver looks at his odometer at two instances while he is driving (as shown below). Given that the diameter of the wheels of the vehicle is 75 cm, what is the average number of revolutions completed by each wheel in 1 minute?


A. 71
B. 283
C. 1200
D. 12700​

A bat is flying at a wall and making a constant 1,70 kHz sound. The bat must fly at a speed of 0.8 m/s in order to detect an 8.00 Hz beat frequency.

The frequency of a repeated event is its number of instances per unit time. It differs from angular frequency and is sometimes referred to as sampling rate for clarification. The unit of frequency is hertz (Hz), or one occurrence per second.

The spring constant of a standing human body is approximately 7.5 Hz, and the rate of a sitting position in a cab is typically 4-6 Hz, according to the research that has already been done. Table 1 displays the natural frequencies of the major body parts.

Frequency = 1.70 kHz

New frequency = 8.00 Hz

V = ?

8.00 / 1700 = 2 * v / 340m/s

v = 0.8 m/s

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If a bicycle and rider has a mass of 50kg if the bicycle has an acceleration of 8 m/s during a 100 m spirit then the force applied is 400 N .

Given is ,

mass (m) = 50 kg

acceleration (a) = 8 m/s²

We know,

force = mass × acceleration

∴ F = m × a

∴ F = 50 × 8

∴ F = 400 Newton

Hence, the force applied is 400 N .

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Since S can be assumed to represent G itself, every finite group is finitely produced. Countable groups need not be finitely generated, but every infinite finitely generated group must be countable.

Any machine that transforms mechanical energy into electricity for transmission and distribution via power lines to residential, commercial, and industrial consumers is known as an electric generator, sometimes known as a dynamo. In addition, generators provide the additional electrical power needed for boats, trains, cars, and other types of transportation. A hydroelectric facility is one where turbine generators are propelled by falling water. Hydraulic motors that produce electricity power electrical generators.

In the event of a power outage, generators are practical equipment that supply electricity, keeping daily tasks or company operations operating smoothly. For usage in a number of applications, generators are available in a variety of electrical and physical designs.

It operates under the principles of Faraday's electromagnetic induction law. According to the faradays law, an electromagnetic field (EMF) is created anytime a conductor is subjected to a changing magnetic field.

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The magnitude of the net upward force exerted on the leaf by the droplet's surface tension is 1.136 x 10⁻³ N.

The net upward force exerted on the leaf by the droplet's surface tension is calculated by applying the following formula as show below.

Mathematically, the formula for surface tension is given as;

γ = F/L

where;

The vertical component of the force is given as;

Fy = F sinθ

γ = F/L

γ = Fsinθ/L

Fsinθ = γL

F = γL / sinθ

The given parameters;

F = (0.073 x 0.011) / sin135

F = 1.136 x 10⁻³ N

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Answer: (a) To find the moment of inertia of Jay about his center of mass, we can use the formula I = mr^2, where m is the mass of the object and r is the distance from the center of mass to the point of rotation. Plugging in the values, we get I = 65 kg * (0.10 m)^2 = 0.65 kg*m^2.

(b) To find the moment of inertia of Jay about the axis of rotation of the chair, we need to use the formula I = Icm + md^2, where Icm is the moment of inertia about the center of mass and d is the distance from the center of mass to the axis of rotation. Plugging in the values, we get I = 0.65 kgm^2 + 65 kg * (0.10 m)^2 = 0.65 kgm^2 + 0.65 kgm^2 = 1.30 kgm^2.

(c) To find the angular acceleration of the chair while Jay is in his cylindrical position, we can use the formula alpha = T/I, where T is the torque and I is the moment of inertia. The angular acceleration is given as -0.0700 rad/s^2, so we can rearrange the formula to solve for T: T = I * alpha = 1.30 kg*m^2 * (-0.0700 rad/s^2).

(d) To find the angular acceleration of the chair while Jay is in his second position, we can use the same formula as before: alpha = T/I. The angular acceleration is not given, so we cannot solve for T directly.

(e) To find the moment of inertia of the chair, we can use the formula I = mr^2, where m is the mass of the object and r is the distance from the center of mass to the point of rotation. The mass of the chair is given as 30 kg and the distance from the center of mass to the axis of rotation is not given, so we cannot solve for I directly.

(f) To find the torque due to friction when Jay is in the chair, we can use the formula T = Fd, where F is the force of friction and d is the distance from the axis of rotation to the point of application of the force. The force of friction is not given, so we cannot solve for T directly.

(g) To find the moment of inertia of Jay in his second position, we need to use the formula I = Icm + md^2, where Icm is the moment of inertia about the center of mass and d is the distance from the center of mass to the axis of rotation. The moment of inertia about the center of mass and the distance from the center of mass to the axis of rotation are not given, so we cannot solve for I directly.

(h) To find Jay's angular speed when the timing started, we need to know the time it took for Jay to complete one revolution and the radius of the circle he was rotating around. Both of these values are not given, so we cannot solve for the angular speed directly.

(i) To find Jay's angular speed just before changing positions, we need to know the time it took for Jay to complete one revolution and the radius of the circle he was rotating around. Both of these values are not given, so we cannot solve for the angular speed directly.

(j) To find Jay+Chair's angular momentum just before changing position, we need to know Jay's angular speed and the moment of inertia of Jay+Chair

Answer:

W= 40 J

P=8 W

Explanation:

solution for work:

w=f d

= 4n (10 m)

= 40 J

Solution for Power

p= w/t

= 40 J/5 s

= 8 W

True. Early snowfall that arrives before the cold winter has frozen the soil generally increases the penetration of water into the soil in the spring.

Early snowfall increases the amount of moisture in the soil, which helps to thaw the soil in the spring and allows for greater water penetration. The extra moisture also helps to insulate the soil from the cold winter temperatures, allowing the soil to remain in an unfrozen state and promoting better root growth and development.

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In this particular que, where four vibrating objects are available, the object that produces the loudest sound is X4.

What are examples of Sound Produced by Vibrations?

In order to understand how sound is produced by vibrations in physics, we must take an example. One of the best examples of sound produced by the vibration of objects is the guitar. In the guitar, we can observe some parallel strings. Here the air is the medium, which helps to produce sound when we create vibration among the strings.

The tuning fork is another widely used illustration that demonstrates how sound may be created by vibrating items. The handle of the tuning fork displays the two melodies. When the tuning fork is struck with the rubber hammer, the air molecules around it are disturbed, which causes vibrations between the two tines and compression or expansion of those molecules. If we repeatedly strike the rubber hammer, they continue to experience either compression or expansion, which causes the production of many waves. Sound travels over space as a result of these waves. This is how vibrating objects make sound whenever a force is applied to the medium or the object.

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The magnitude of the vector [tex]\vec C[/tex]  is 8.6.

A - B  is used to indicate the vector subtraction of two vectors a and b, and it simply involves adding the vector's negative for vector b.

given :

A = 5.7

angle from x axis = 90 -38 = 52

[tex]\vec A =[/tex] ( 5.7 cos 52,  5.7 sin 52)

B = 4.3

[tex]- \vec B[/tex] angle from x axis = 90 +24 = 114

[tex]- \vec B[/tex] = (4.3 cos 114 , 4.3 sin 114)

[tex]\vec A - \vec B = \vec A + ( - \vec B)[/tex]

= ( 5.7 cos 52,  5.7 sin 52) +  (4.3 cos 114 , 4.3 sin 114)

=( 5.7 cos 52 +4.3 cos 114 , 5.7 sin 52+ 4.3 sin 114)

= (3.51 - 1.75, 4.49+3.93)

[tex]\vec C[/tex] = (1.76, 8.42)

magnitude of [tex]\vec C[/tex]  = [tex]\sqrt{1.76^2+ 8.42^2}[/tex]

=[tex]\sqrt{3.10+70.9}[/tex] =[tex]\sqrt{74}[/tex] = 8.6

The magnitude of the vector  [tex]\vec C[/tex] is 8.6.

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Pressure on the bottom when water is added to fill the pipe to its top is 180kPA.

In the first scenario, the atmospheric pressure is:

In the second scenario, h = 8m + 1 m. Therefore, the pressure at the bottom of the barrel is:

What is hydrostatic pressure meaning?

Hydrostatic pressure refers to the pressure that any fluid in a confined space exerts. If the fluid is in a container, there will be some pressure on the wall of that container.

What is hydrostatic pressure used for?

Hydrostatic pressure is one reason (along with the lack of oxygen) why it's not safe for humans to travel unprotected in space. You rely on hydrostatic pressure to keep your lungs at the right inflation and to keep the water in your body from vaporizing.

How is hydrostatic pressure calculated?

The pressure in a liquid at a given depth is called hydrostatic pressure. This can be calculated using the hydrostatic equation:

P = rho * g * d, where P is the pressure, rho is the density of the liquid, g is gravity (9.8 m/s^2) and d is the depth (or height) of the liquid.

Thus, the pressure on the bottom when water is added to fill the pipe to its top is 180kPa.

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The properties of manganese oxide, which has two oxygen atoms for every manganese atom, are discussed in this answer.

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The maximum angle will be 67°.

Solution:

= 0.0088 = 0.0147(1 - cos∅)

= 0.59 = (1 - cos∅)

= cos∅ = 1 - 0.59

= ∅ = cos⁻¹(0.4) = 67°

When the angle of incidence on water reaches a certain critical value the refracted ray lies along the boundary and the refraction angle is 90 degrees. This angle of incidence is known as the critical angle. This is the maximum angle of incidence at which refraction can occur.

The velocity of the incident particle before impact is parallel to the velocity of the center of gravity. Therefore, the maximum deflection angle is equal to the maximum angle between the velocity of the center of mass and the velocity of the incident particle after the collision as shown below.

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Answer:

9.6

Explanation:

v² = u² + 2as

v² = 0 + 2(9.81)(4.7)

v² = 92.214

v = 9.6 m/s

The force exerted by gravity on a mass of 6.5 kg will be equal to 64 N. Hence, option A is correct.

Any operation that has the ability to alter, maintain, or modify a body's motion is considered a force in mechanics. Isaac Newton's Principia Mathematica has three laws of motion that are usually used to demonstrate the idea of force (1687). A body at rest or consistently moving in a straight path is said to remain in that state before a power is applied to it, according to Newton's first law.

Now, let's find out the force exerted by gravity,

Given,

Mass, m = 6.5 kg

Use the value of acceleration due to gravity (g) as 9.8 m/s².

f = 6.5 × 9.8

f = 63.7 or,

f = 64 N.

Therefore, the force exerted by the gravity will be equal to 64 N.

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A cylinder 8.0 cm tall and 1000 kg/m3 in mass floats in clear water with its axis perpendicular to the surface. Its mass density is 0.8375. The cylinder is 1.3 cm long when it is above water.

The substance's mass per unit of volume is its density (also known as specific mass or volumetric mass density). The Latin letter D can also be used to represent density, however the most common symbol is (the lower case Greek letter rho). According to mathematics, density is determined by dividing mass by volume, where denotes the density, m denotes the mass, and V denotes the volume. An assertion of the perpendicular axis theorem The moment of inertia, for any axis that is perpendicular to the plane, is stated by the perpendicular axis theorem.

(8.0 - 1.3)/8.0 = 0.8375

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The complete question is -

a 8.0 cm -tall cylinder floats in pure water (density 1000 kg/m3) with its axis perpendicular to the surface. the length of the cylinder above water is 1.3 cm.  What is the cylinder's mass density?

All of the potential energy has been converted to kinetic energy at the base of hills, resulting in greater speed. Potential energy = 735000 J ; kinetic energy = 0 J (option -C) is correct answer.

At the bottom of hills, roller coaster cars always move the fastest. This is connected to the first idea in that at the base of hills, all potential energy has been transformed into kinetic energy, leading to increased speed.

At a height of 0 meters,

Potential energy = mgh

Potential energy = 2,500×9.8×30

Potential energy = 735,000 J

Kinetic energy = 1/2mv²

Kinetic energy = 1/2×2,500×0

Kinetic energy = 0.

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The electric potential at the fourth corner (point A) is E4 = kQ.[ 2/a2 + 1/a√2 ]

The electric potential is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in an electric field.

Number of point charges = 3

Using the superposition principle to calculate the net electric field at the fourth point, so

E4 = E1 + E2 + E3

E4 = kQ/a2 + kQ/√(2a2) + kQ/a2

E4 = kQ.[ 1/a2 + 1/√(2a2) + 1/a2 ]

E4 = kQ.[ 2/a2 + 1/a√2 ]

Therefore the electric field at the fourth corner is  E4 = kQ.[ 2/a2 + 1/a√2 ].

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Complete question:

Three-point charges are arranged at the corner of a square of side l as shown in Fig. 17-39. what is the potential at the fourth corner (point A)?

3200kg-m²s⁻² the kinetic energy of the dog which is 16Kg mass and moving with 20m/s velocity.

Kinetic Energy the energy possessed by the body due to the motion of the object. Si unit of kinetic energy is Joule or kg-m²s⁻². And it is denoted by K.E

Formula of Kinetic Energy is (KE) = 1/2mv²where as m= Mass and                 v= Velocity

m= 16kg mass of the dog

v =20m/s velocity of the dog, substitute these values in formula

K.E =1/2(16)(20)² = 3200 Kg-m²/s².

Hence the kinetic energy of the dog which is having mass of 16kg and running at a velocity of 20m/s is 3200J.

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16kg dog is moving with a velocity of 20m/s.

We know that the kinetic energy of a body is the energy possess by it due to its motion

So,

K=1/2mv^2

where,

K is kinetic energy

M is mass

V is velocity.

By substituting the values,

K= 1/2 * 16 * 20 *20

K = 6400/2

K = 3200J

So the kinetic energy of dog is 3200J.

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The correct matches for the given words are:

1. grand unified theory - predicts the strong, weak, and electromagnetic forces

2.electroweak force

3. Inflation

4. Olbers' paradox

5. cosmic microwave background

6. annihilation

Physical interactions between electrically charged particles are known as the electromagnetic force. It is the result of the interaction of all magnetic and electrical forces and operates between charged particles.

Both visible light and radiation in other wavebands that the human eye cannot see are produced by the electromagnetic field.

A faint glow of light known as the Cosmic Microwave Background radiation, or CMB for short, permeates the entire cosmos and falls on Earth with a remarkably consistent intensity from all directions.

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By the time Ernie arrives at Burt, the log has travelled 0.3 metres in relation to the coast.

define mass ?

The density and kind of atoms in any specific thing are referred to as the object's mass in science. Although mass can also be measured in pounds, the kilogramme (kg) is the SI unit of mass (lb).

Think of a pillowcase stuffed with feathers and one packed with bricks to rapidly grasp the notion of mass. Which one is heavier? The bricks have a larger mass because their atoms are heavier and denser. Because of this, although though both pillowcases are the same size and level of fill, one has a significantly higher mass than the other.

In this case, the mass is denoted by (m), while the distance is denoted by (x).

The 3.9m-long log weighs 260kg and is long. Burt weighs 30 kg, whereas Ernie weighs 40.5 kg.

Ernie accepts Burt's offer of a cookie and moves to his side of the log to take it.

By the time Ernie gets to Burt, the log should have travelled x metres. Consequently, using the formula above,

30(x)+260(X)+40.5(x-3.9)

≈0.3

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The equation use to solve these problem is the equation for total energy. Hence option 1 is correct.

Total energy is defined as the overall amount of energy used in a certain branch or variable. Because energy data is recorded directly rather than as the result of an activity level and an energy intensity, total energy can be distinguished from final energy intensity.

The object has a maximum amount of gravitational potential energy at the top of the roller coaster and zero kinetic energy. The gravitational potential energy of the object starts to decline as it starts to descend to the bottom, but the kinetic energy starts to rise.

Thus, the equation use to solve these problem is the equation for total energy. Hence option 1 is correct.

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The minimum force of friction required to hold the system of Figure in equilibrium is 50 Newton.

What is frictional force?

Frictional force is the force produced when two surfaces slide against and touch each other. The surface texture and amount of force needing them together have the biggest an impact on these forces. The amount of frictional force is influenced by the object's position and angle.

The forces of adhesion between the sites of contact areas of the surfaces, which are always minutely uneven, are the primary cause of friction between objects. The action of the imperfections of the harder surface tilling across the softer surface shears these "fused" connections, causing friction.

If an object is placed against an object, then the frictional force will be the same as the weight of the object. If an object is pushed against the surface, then the frictional force will be increased and become extra than the weight of the object.

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Answer: 1.0 m/s2

Explanation:

This is a Newton's 3rd Law of Motion problem.  The force applied on the box by the skater must equal the force applied on the skater by the box (and in the opposite direction).  F = ma

Let x = acceleration of the skater

(15.0 kg)(4.0 m/s2) = (60.0 kg) (x)

x = 60 N / 60 kg = 1.0 m/s2

The thrust force that is acting on the rocket engine is obtained as  5782 kN.

We know that the thrust is the force that is acting on an object that enables the object to be able to move higher. The thrust force can be applied to a rocket such that the rocket can be able to move higher and then pass through the air.

This implies that the thrust force is about the most important force when we want to be able to launch a rocket or when we are trying to move an aeronautical engine. In this case, we are asked to be able to obtain the thrust force as we can see from the parameters that have been given.

We now know that the thrust force can be obtained as; 118kg * 9.8 m/s^2 * 5000m/s = 5782 kN

There would be a thrust of  5782 kN working on the engine.

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The magnitude of the shop B is 15.62 m and the direction will de same as given.

Magnitude is defined as the direction and size of an item at its largest. It reveals the absolute or relative size or direction that an object moves when in motion.

The product of vw -  vs determines the relative velocity of a ship to water.

To calculate the magnitude we use formula

Magnitude = √vw² + vs²

Magnitude = √ 12² + 10²

Magnitude = √ 144 + 100

Magnitude = √ 244

Magnitude = 15.62 m

Thus, the magnitude of the shop B is 15.62 m and the direction will de same as given.

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​

Refer to the photo taken

The superposition principle's implication that distinct wave displacements alter every location at every instant in time is known as interference.

Water moves in a circular pattern as a result of energy traveling through it, creating waves. Water somehow doesn't, however, literally move in waves. In the ocean, waves carry energy rather than water, and if there is nothing in their path, they have the capacity to span a whole ocean basin.

A wave is an energetic disruption in a fluid that doesn't include any net particle motion. Elastic deformation, a change in pressure, a pulsed electromagnetic intensity, an electric potential, or a change in temperature are a few examples.

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The magnetic field associated with the coil will change as it is moved near a stationary magnet, which will generate current in the coil. Galvanometer in Region C exhibits deflection in one direction as a result of this.

Electrical charge carriers, often electrons or atoms deficient in electrons, travel as current. The capital letter I is a typical way to represent current. The ampere, denoted by the letter A, is the common unit. A stream of charged particles, such as electrons or ions, travelling through an electrical conductor or a vacuum is known as an electric current. The net rate of electric charge flowing through a surface or into a control volume is how it is calculated.

Charge is movable and can freely flow in certain substances, known as conductors. Conductors include metals and a select few additional elements and compounds. Copper, aluminium, and most other metals are examples.

The majority of its uses are low voltage ones, such aeroplane applications and battery charging. Appliances for both domestic and industrial and commercial use run on alternating current. Amperes are used to measure electric current

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