How does the kinetic theory explain the following? (a) A gas exerts a pressure on its container walls. (3marks) ​

The moment of inertia for a disk with mass of 500g and radius of 12cm rotated about its diameter is 7.2 × 10-³kgm².

Moment of inertia is a measure of a rigid body's resistance to change in its angular velocity around a given axis.

The formula for the moment of inertia is the “sum of the product of mass” of each particle with the “square of its distance from the axis of the rotation”. The formula of Moment of Inertia is expressed as follows:

I = mr²

Where;

According to this question, a disk with mass of 500g and radius of 12 cm rotated about its diameter. The moment of inertia can be calculated as follows:

I = 0.5kg × 0.12²m

I = 7.2 × 10-³kgm²

Therefore, 7.2 × 10-³kgm² is the moment of inertia of the disk.

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The time taken by the ball is 0.30s.

We know that the horizontal velocity has to do with the speed of the object has it moves along a horizontal path. In this case, we can see that the ball is thrown horizontally with a velocity of 12m / s. We have also been told in this question as we have it here to assume that there was no air resistance that is involved.

Thus we have;

Horizontal speed of the ball =  12m / s

Distance covered by the ball =  3.5 m

Let us see that;

V = s/t

V = speed

s = distance

t = time

t = s/V

We should now have;

t = 3.5 m/12 m/s

t = 0.30s

We can now see that the time that t would take the ball to hit the ground is 0.30 seconds of time.

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Answer:

Explanation:

Given:

Vₓ = 12 m/s

H = 3.5 m

g = 9.8 m/s²

__________

t - ?

According to the principle of independence of motion, we find the fall time from the formula:

H = g·t²/ 2

t = √ (2·H / g)

t = √ (2·3.5 / 9.8 ) ≈ 0.85 s

Correct answer:

C.  0.85 s

Answer:

The answer is 9.32x10^(-6) T.

Explanation:

The formula of finding magnetic field in a long solenoid is (B)= (MU)X N X I/L.

MU=4*(PI)*10^-7 h/m

n=1255

i=4.2 A

l=0.71 m

b= 9.32*10^(-6) T.

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The work done by friction when a crate of 263 kg slides 3.2 m is 1072.2 J.

Friction is the force that opposes the motion of two bodies in contact.

To calculate the work done by friction, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the work done by friction is 1072.2 J.

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Neutrinos generated in the core of the sun travel to the surface so quickly, compared to gamma ray photons because they don't interact with electromagnetic forces.

Neutrinos are neutral, massless particles. Because of their lack of mass, neutrinos can travel through space faster than photons. They have no electric charge, so they don't interact with electromagnetic forces. They also have no strong interactions and only weak ones, which means they can pass through matter without interacting with it at all.

Gamma rays are another type of radiation that originates from nuclear reactions in stars like our sun. however, photons are affected by gravity and other forces just like any other particle would be when moving at these speeds. They're also absorbed by matter much more readily than neutrinos are because they do interact electromagnetically with other particles around them.

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Answer:

sound wave's amplitude relates to the change in pressure caused by the wave measured at a specific location. The sound is perceived as louder if the amplitude increases, and softer if the amplitude decreases.

The new acceleration would be 5.62162m/s²

Given - acceleration a=8m/s²

As per question force = F/3.7

and mass = m/2.6

To find :- new acceleration α°

Formula: F=ma

Calculation : F/3.7= [mα°]/2.6

Divide these 2 equations

2.6= 3.7(α°/a)

α°= 2.6 x 8 / 3.7

α°=5.62162m/s²

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The direction should approach the helicopter is the downhill side.

The Federal Communications Commission controls and regulates all interstate and international radio television wire satellite and cable communications within the United States. Typically the helicopter is approached from the front or sometimes from the side, within the pilot's line of sight. Never approach from behind. Never approach a downhill helicopter. Main he could step into the rotor.

Choose your way to the machine on level ground or uphill. Always approach helicopters from the downhill side. Rotor separation is greatly affected by slopes. To avoid the main rotor and other components of the described communication system taking off by approaching the sloping side of the sloping landing site.

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We are given with a case of a moving shopping cart.

We are asked , how to increase the time, change the force.

For that, if we reduce the applied force in order to increase the time interval.

Generally, if we know the force applied and time taken, we can calculate the change in momentum.

As, Force, F = dP/dt

i.e. Rate of change of momentum w.r.t. time is Force.

So, dP = F.dt

Unit of Force is Newton, N in MKS (metre kilogram second) system.

Unit of Force is Dyne in CGS (centimetre gram second) system.

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The resistivity rho of the piece of the wire will be 1.60 × 10⁻⁸ Ωm. So, the material is copper wire.

Copper is the electrical conductor in many categories of electrical wiring. Copper wire is used in power generation, power transmission, power distribution for telecommunications, electronics circuitry, and countless types of electrical equipment.

The resistivity of a material is the resistance of a wire of that material of unit length and unit area of cross-section. Its S.I. unit is ohm-metre.

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The change in the kinetic energy of this object is 600 J, when an object of mass 10 kg is initially at rest, and 100 N force cause it move horizontally at a distance of 6 m.

Mass of the object = 10kg

Force = 100N

Distance = 6m

Change in kinetic energy of this object =Δ KE

Expression for the change in the kinetic can be given as follows:

Δ Kinetic Energy = W

,W is the workdone on the object.

This is given by the formula below,

W= F *d

Hence,

Δ KE = F × d

Δ K.E= (100N × 6m)

Δ K.E. = 600Nm

Δ K.E. = 600 Joule

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The key observation enabled Edwin Hubble to prove this by observing individual Cepheid variable stars in Andromeda and applying the period-luminosity relation.

American astronomer Edwin Powell Hubble lived from November 20, 1889, through September 28, 1953. He was a significant contributor to the development of observational cosmology and extragalactic astronomy.

Hubble established that many objects formerly believed to be "nebulae" or clouds of gas and dust, were actually galaxies outside the Milky Way. He scaled galactic and extragalactic distances using the strong direct correlation between a classical Cepheid variable's luminosity and pulsation time, which was found in 1908 by Henrietta Swan Leavitt.

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The speed of the roller coaster when it comes at the top of the second hill is 17.32 m/s.

The mass of the roller coaster is 500 kg and it is travelling with a speed of 10m/s.

Firstly the roller coaster ride pass a height of 20 m and after that it goes down and then climb till height of 10 m.

It has been know that throughout the motion the total mechanical energy is always conserved.

So we can write,

Potential energy at the top of the 20 m + kinetic energy at the top of 20 m hill = potential energy at the top of 10 m hill + kinetic energy at the top of 10m hill.

MgH + 1/2MV² = Mgh + 1/2Mv²

H is 20m and h is 10m, while M is mass of roller coaster and V is the speed at top of 20m hill and v is the speed at top of 10m hill.

Putting all values,

g(H-h) = 1/2(v²-V²)

10×10 = 1/2(v²-100)

v = 17.32 m/s.

So, the speed of the roller coaster at the top of 10m hill is 17.32 m/s.

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4.80m is the far of the recipients must goods dropped.

The speed of an object is the rate at which it moves through space. A slow-moving object travels a relatively short distance in a given amount of time, whereas a fast-moving object travels a long distance in a short amount of time.

A)Since we are aware that the plane's vertical speed is zero

In this instance, the mass is dropped with no beginning speed.

thus, we will

y=1/2gt²

235=1/2(9.81)t²

t=6.92s

Consequently, it is given as the horizontal distance it moved.

d=vt

d=(69.4)(6.92)

d=480.4m

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With a negative acceleration, the skateboard's beginning velocity will be higher than its end velocity.

The correcty answer is 1

Based on the assumption that the object's energy is conserved, its velocity equals the square root of twice square product of the its acceleration or the distance it travels. This relationship also depends on the object's initial velocity.

When gravity first exerts force on an object, its initial velocity indicates how quickly it moves. The final velocity, on the other hand, is a vector quantity that determines the rate and direction of the a moving body when it has reached its maximum velocity.

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As a result of the collision, the cart, which had a velocity of 1, comes to rest. The cart then accelerates with velocity v1 from rest. assuming that a moving cart collision elastically with a stationary cart.

We are aware that both the linear momentum and the kinetic energy are conserved in completely elastic velocity. However, only the kinetic energy of an inelastic impact is conserved. Any situation in which two or more bodies quickly exert forces on one other is referred to be a collision. The scientific definition of the word "collision" makes no reference to the magnitude of the force involved, despite the fact that the most frequent usage of the word relates to instances in which two or more objects clash violently.

The instantaneous speed could be compared to the speed shown by the speedometer.

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.

One way to avoid EMI problems is to use fluorescent lights. Option B.

Fluorescent lights deteriorate quickly especially if they are installed in a place where they are turned on and off frequently. Fluorescent lights shorten their life each time they are turned off and on. This can lead to premature failure and you will end up spending more money replacing bulbs more often.

EMI from fluorescent lighting systems is rare. Designers considering the use of electronic ballasts can greatly reduce the potential for EMI problems with careful planning. EMI is caused by the close relationship between electricity and magnetism. Any flow of electricity creates a small magnetic field. Conversely when the magnetic field moves an electric current is generated.

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When plates commute in the exact direction it collides, and the plates move to other at convergent boundaries.

The lighter, dense, and much more elastic oceanic plate dips underneath the thicker, more stiff continental plate whenever a continental plate encounters a marine plate.

It's known as subduction. Deep ocean trenches, like the one that runs down South America's west coast, are created by subduction.

The continent's undercut rocks start to melt. On occasions, a chain of eruptions forms as the hot magma rises to the surface and travels through the continent.

Nearly 80% of earthquakes happen along convergent borders when plates are being pushed together.

Destruction, when two continental plates crashes, is just another kind of convergent boundary. The plates collapse and are propelled upward since neither is heavier compared to the other.

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The speed of the longitudinal wave is 1.584 or approximately 1.6 meters per second.

Longitudinal waves are waves in which the medium's vibration is parallel to the wave's travel direction and the medium's displacement is in the same direction as the wave's propagation.

Sound waves are one example of longitudinal waves. Waves of ultrasound P-waves from earthquakes

A longitudinal wave's key features include compression, rarefaction, wavelength, amplitude, period, and frequency.

To calculate the above answer multiply wavelength by frequency to get the speed of a wave.

That is:

2.4 x 0.66

= 1.584

Where the frequency is not given beforehand, you can divide 6 crests by 9.1 seconds to determine the frequency.

Hence, the speed of the longitudinal wave is 1.584 which is approximately 1.6.

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a point on the circumference travel if the wheel is rotated through angles of 30 rad is 7.8m

4.9 x [tex]10^{7}[/tex] revolutions  if the car travels 80000 km.

The Radius of the tyre = 0.26 m.

Perimeter = 2[tex]\pi r[/tex] =0.52[tex]\pi[/tex]m

When the circle is rotated through an 30rad angle, a point of its circumference travels a distance equal to an 30rad arc of this circle.

a full revolution is 2π rad, then an 30rad angle represents

30/2[tex]\pi[/tex] =15/[tex]\pi[/tex]

15/[tex]\pi[/tex] * .52 [tex]\pi[/tex] = 7.8 m

d =  7.8 m.

the car travels 80000 km

revolutions do the tires = 80000 * [tex]10^{3}[/tex]/ 0.52[tex]\pi[/tex]

=4.9 x [tex]10^{7}[/tex] revolutions.

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An example of  supplementary light source that you might bring to a photo shoot as a photographer is a : separate flashlight.

The flash is very important in photography because it acts as a second light source. It fills in areas where the image is underexposed due to the metering mode of camera prioritizing a different part of the frame, such as the sun in the photo below.

Professional photographers use a flash light frequently, although not the pop up flash on the camera. Photographers generally use an off camera strobe. Common reason to use flash unit is low-light indoor environments.

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Since the meter's 3V terminals are connected to the circuit, we have to read the "zero-to-3" scale on the meter to get our measurement.  That's the scale under the marks.

On that scale, the needle points to  1.4 DC Volts.  That's the potential difference between the two points the meter probes are touching.

The pressure in the gas at that point is equal to the initial pressure, 100 kPa.

To expand adiabatically, there must be no heat transfer involved. Adiabatic expansion means that no heat is transferred between the gas and its surroundings; this means that if we double the volume of our gas, nothing should change in terms of temperature as long as there is no heat transfer to or from our system during expansion.

Since we're starting out with a monatomic ideal gas, we know that its entropy is going to stay constant throughout this process, so the ideal gas law gives us a relationship between pressure, volume, and temperature: PV = nRT

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3.74 m/s is  the speed of the cart of mass 2.0 kg and the string gives a centripetal force of 40. N.

The force that creates centripetal acceleration is known as centripetal force. All objects in uniform circular motion accelerate toward the center of the circle, and as a result, they must likewise experience a force from the center. The centripetal force is that force.

Briefing :

Given ,The mass of the cart, m = 2 kg,

The standard equation would be F = ma , where a is acceleration, f is force, and m is mass. However, the breaking strength of the string is 40 N.

a   =    [tex]\frac{v^{2} }{r}[/tex]

F   =   ma

F   =   [tex]\frac{mv^{2} }{r}[/tex]

40 =   [tex]\frac{2v^{2} }{0.70}[/tex]

[tex]v^{2}[/tex]  =   14

v   =  [tex]\sqrt{14}[/tex]

v  =  3.74 m/s

Therefore , the speed of the cart is 3.74 m/s .

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One of the brightest nebulae in the night sky, the Orion Nebula may be seen with the unaided eye. The Trapezium is a young open cluster of four main stars in this magnitude 4 interstellar cloud of ionized atomic hydrogen.

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Astronomers have examined rich clusters of galaxies with their instruments, They have found that these clusters have giant elliptical galaxies than poor clusters

Elliptical galaxies are the most abundant type of galaxies found in the universe but because of their age and dim qualities, they're frequently outshone by younger, brighter collections of stars.

Elliptical galaxies lack the swirling arms of their more well-known siblings, spiral galaxies. Instead, they bear the rounded shape of an ellipse, a stretched-out circle.

One of the most famous elliptical galaxies is Cygnus A, which is located roughly 600 million light-years from Earth and is an extremely bright radio source. Cygnus A is not only well-known to astronomers, but has a place in science fiction; it was featured in the 1985 novel "Contact," a Carl Sagan story that later inspired a Hollywood movie of the same name.

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Answer:

Light can travel through a glass or through a vacuum

The velocity of the fluid where the pipe is narrow s 46.36m/s.

The diameter of the larger end of the constriction pipe is 6.5 cm and the diameter of the narrow end of the pipe is 2.7cm.

According to equation of continuity, the volume of the fluid incoming is equal to the volume of the fluid outgoing.

So, we can write,

A₁V₁ = A₂V₂

A₁ and V₁ are the area and speed at the larger end and A₂ and V₂ are area and speed at the narrow end.

Putting values,

π(6.5/2)².8 = π(2.7/2)².V

V = 46.36m/s

The velocity of the fluid where the pipe is narrow is 46.36m/s.

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At 7.1 Hz a 200-turn, flat coil of cross sectional area of 300.0 cm2 be rotated in a uniform 30.0-mt magnetic field to have a maximum value of the induced emf equal to 8.0 v

An electric charge, an electric current, and magnetic materials are all affected magnetically by a magnetic field, which is a vector field. A force perpendicular to the magnetic field and its own velocity acts on a moving charge in a magnetic field.

Given,

number of turns is N = 200 turns

cross-sectional area is A = 300 cm² = 300 x 10⁻⁴ m²

the magnitude of magnetic field strength is B = 30 x 10⁻³ T

the maximum value of the induced emf is E = 8 V

Now,

Maximum induced emf is, E = NBAω

where,

ω is the angular velocity (ω = 2πf)

Now,

E = NBA2πf

where,

f is minimum frequency

So, f = E / (NBA2π)

f = 8 / (200 x 30 x 10⁻³  x 300 x 10⁻⁴ x 2 x 3.142)

f = 7.073 Hz

f = 7.1 Hz

∴ the minimum frequency of the coil is 7.1 Hz.

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The x component of the object's velocity is -8 m/s and the y component of the object's velocity at the given time is 7 m/s.

option B is the correct answer

The x and y components of the object's velocity at the given time is calculated as follows;

x = -3t³ - 5t²

y = 4t² + 3

where;'

At the given time, t = 1 second, the  x and y components of the object's velocity is;

x = -3(1)³ - 5(1) = -8

y = 4(1)² + 3 = 7

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