a solid sphere of mass m and radius r rolls without slipping along a table at speed v. what is its kinetic energy? (given for solid sphere i

There are several reasons why you might want to keep your engine running when you are waiting to pick up your husband, even if you could stop the engine to save gas.

One reason is that keeping the engine running allows you to use the car's electrical systems, such as the lights, air conditioning, and wipers, without draining the battery. If you turn off the engine and use these systems, the battery will eventually drain, and you may have to jump-start the car to get it running again.

Another reason is that turning off the engine and restarting it can be hard on the engine and may reduce its lifespan. When you turn off the engine, all of the internal components come to a stop and may experience wear and tear when the engine is restarted. By keeping the engine running, you can avoid this additional wear and tear.

Finally, keeping the engine running may be more convenient and safer. It allows you to keep the car's systems running and be ready to drive at a moment's notice, which may be important if you are waiting in a potentially dangerous or unfamiliar location.

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According to the first law of thermodynamics, the total amount of energy in the universe constant .

The First Law of Thermodynamics is a thermodynamic adaptation of the Law of Conservation of Energy. "The total energy in a system remains constant, even when it may be transformed from one form to another," is a straightforward expression. "Energy cannot be created or destroyed" is another frequently used phrase (in a "closed system"). This is the fundamental tenet of the First Law, while there are numerous nuances and consequences that might be better expressed in more intricate forms.

It distinguishes between heat and thermodynamic work as two different types of energy transmission for a system with a constant amount of matter. The law also specifies a system's internal energy, a broad attribute for accounting for the balance of energies.

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A bookshelf is 2m long, with support at it end (P and Q). Don't consider the weight of the bookshelf. The book is moved to that it is 50cm from Q. The force at P is W/3 and Q is 2W/3.

The force at points P and Q using the concept of moments, you need to know the weight of the bookshelf and the location of the book on the shelf. The moment of a force about a point is equal to the force multiplied by the distance from the point to the line of action of the force. The line of action of a force is the straight line through which the force acts. In this case, let's assume that the weight of the bookshelf is W and the location of the book is x meters from Q. The forces at points P and Q can be found using the following equations:

Moment at P = (W - F) x x

Moment at Q = F x (2 - x)

Where F is the force exerted by the book on the shelf.

Solving these equations for F and substituting the given values gives:

= F = W x (2 - x) / (2 - x + x)

= W x 2 / 3

The force at point P is equal to the weight of the bookshelf minus the force exerted by the book, which is:

= F at P = W - F

= W - W x 2 / 3

= W / 3

The force at point Q is equal to the force exerted by the book, which is:

= F at Q = F

= W x 2 / 3

So, if the weight of the bookshelf is W and the book is 50 cm from Q (which is equal to 0.5 meters), the force at point P is W / 3 and the force at point Q is 2W / 3.

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A concave mirror having a focal length of magnitude 5.0 cm forms an image 4.0 cm behind the mirror. Thing that is present in front of the mirror is the object for this image.

A mirror with a curved reflecting surface is referred to as a curved mirror. The surface could be concave mirror or convex (bulging outward) (recessed inward). Although optical systems occasionally employ alternative shapes, most curved mirrors have surfaces that are formed like a portion of a spherical. Since spherical mirror systems, like spherical lenses, are subject to spherical aberration, the most prevalent non-spherical variant is found in optical instruments such as reflecting telescopes that must picture distant objects. Mirrors that distort images are used for amusement. Concave and convex sections on them provide purposefully distorted images. When the object is positioned at specific distances, they also offer images that are either magnified or greatly diminished (smaller). A curved mirror with a reflective surface that bulges in the direction of the light source is referred to as a convex mirror or diverging mirror. Convex mirrors do not focus light since they reflect it outward. Since the focal point (F) and the center of curvature (2F) are both fictitious positions "within" the mirror that cannot be reached, such mirrors always produce a virtual image.

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The radius of the sphere is 0.065 meters

        Volume of the sphere: [tex]\frac{6 kg}{5000kg/m^{3} }[/tex] = 0.0012 [tex]m^{3}[/tex]

  3. Calculate the radius from the volume.

      The volume of sphere is defined with [tex]\frac{4}{3}[/tex] x [tex]\pi[/tex] x [tex]r^{3}[/tex]

From step 2, the volume is 0.0012 [tex]m^{3}[/tex]    so it can be written like this :

Volume =  [tex]\frac{4}{3}[/tex] x [tex]\pi[/tex] x [tex]r^{3}[/tex]

0.0012 =  [tex]\frac{4}{3}[/tex] x 3.14 x [tex]r^{3}[/tex]

   [tex]r^{3}[/tex] = [tex]\frac{0.0012 x 3}{4 x 3.14}[/tex]

[tex]r^{3}[/tex] = [tex]\frac{0.0036}{12.56}[/tex] = 0.000286

r = [tex]\sqrt[3]{0.000286}[/tex] = 0.065 meters

Thus, the radius of a sphere that has a density of 5000 kg/m3 and a mass of 6.00 kg is 0.065 meters.

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10 to the power 6 grams is the mass of 235u that, when undergoing induced fission, would produce the same amount of thermal energy as 1 tonne of coal.

The process of nuclear fission involves the splitting of an atom's nucleus into two or more smaller nuclei. Even by the energetic standards of radioactive decay, the fission process releases a very high quantity of energy and frequently results in gamma photons. German chemist Otto Hahn and his assistant Fritz Strassmann made the discovery of nuclear fission of heavy elements with the help of Austrian-Swedish physicist Lise Meitner. Hahn recognized that there had been an atomic "burst."  Meitner and her nephew Otto Robert Frisch conceptualized it in January 1939. Frisch gave the procedure its name using the analogy of biological cell division. Nuclear fission is an extremely dense source of energy because the quantity of free energy present in nuclear fuel is millions of times more than the amount of free energy present in an equivalent mass of chemical fuel, such as gasoline. Nuclear waste is a problem because the byproducts of nuclear fission are, on average, far more radioactive than the heavy elements that are typically fissioned as fuel and stay so for long periods of time. Plutonium is created by neutron absorption that does not result in fission from 238 U, as well as small actinides from both 235 U and 238 U.

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The forces that the book exerts on the earth because it describes the same interaction.

A book on a table exerts a downward force on the table, and the table exerts an upward reaction force on the book. The book remains stationary because the forces are equal and opposite. These forces are the earth's gravitational pull exerting a downward force and the pressure of the table against the book.

Because the force exerted by the table on the book is the same and opposite to the force exerted by the earth. Yes, action-reaction exists in this case. The book exerts a force on the table that acts on the book due to gravity. At the same time, the table exerts an equal and opposite force on the book. So the book is fixed on the table.

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Friction is an opposition force acting on the surface of the body that tries to oppose the motion of the body. its unit is Newton (N) . The minimum coefficient of static friction is k= αtanβ.

It is a particular form of opposing force that is acting on the body's surface and seeks to stop the body from moving. its measure is in Newton (N). It is described mathematically as the result of the friction coefficient and normal reaction.

The equation becomes balanced once the specified force and acceleration have been resolved in each of the individual components.

X-directional components

On an incline, find the acceleration

Masina -F= ma

mgcosa =R

F=ur

Slippage must be prevented by a frictional force that is less than the maximum static friction force. We'll use constants like to represent the proportion between the opposite and adjacent sides of the ramp. At this point, ma equals the frictional force. Previously, a=gsin was found to exist. Equating both terms:

αmgsinβ = Kmgcosβ

K= α(sinβ/cosβ)

sinβ/cosβ= tanβ

k= αtanβ

Thus, the minimum coefficient of static friction is k= αtanβ.

A bowling ball rolls without slipping up a ramp that slopes upward at an angle β to the horizontal. Treat the ball as a uniform, solid sphere, ignoring the finger holes.a. What is the acceleration of the center of mass of the ball?b. What minimum coefficient of static friction is needed to prevent slipping?

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A satellite travelling at 3600 km per hour in a stable circular orbit around the earth has a speed of 6320 m/s.

Utilizing mass (of the earth and satellite) and the separation between the satellite and the earth's core, one can calculate the gravitational pull (or force) between a satellite and the earth.

The gravitational equation is v = √GM/r, where

v = orbital velocity (m/s)

G = 6.67x10-11Nm2kg2 (gravitational constant)

M is the orbiting body's mass (kg)

orbital radius, r (m)

5.97 x 10^24 kg is the Earth's mass, or M.

r = height + Earth's radius equals (6370 + 3600) x 10^3 = 9970 x 10^3 = 9.97 x 10^6 m

v = (6.67 x 10-11) x (5.97 x 10^24) / (9.97 x 10^6) = 6320 m/s

Hence speed of satellite is 6320m/s

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A grating's resolving power will rise as the number of lines increases.

The peak intensity of the grating intensity expression is related to the square of the number of illuminated slits. The diffraction maximum becomes sharper and much more intense with additional slits, in addition to being much more intense overall. As a result, a grating with a high resolving power may discriminate between minute wavelength changes. Thus, we can improve the diffraction grating's resolution by increasing the number of slits. You get more damaging interference when you use more slits. On the other side, because of more constructive interference, the maxima grow more brighter. This significantly improves the experiment's resolution, making it simpler to quantify the interval between consecutive maxima.

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The standing wave and sound wave have the same frequency

When a guitar string is plucked or strummed, it vibrates and creates a standing wave pattern. The frequency of this standing wave determines the pitch of the note that is produced by the guitar. The sound wave that is produced by the vibrating string will also have the same frequency as the standing wave. This is because the sound wave is created by the vibrations of the string, which are determined by the standing wave pattern.

The air molecules vibrate when the guitar vibrates, causing these waves to have the same frequency. Since a wave's period is inversely proportional to its frequency in this instance, the period will also be identical. Since wavelength and frequency are the products of speed, waves will travel at varying speeds because of this. As a result, both the period and frequency are identical.

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The value of the resistor is 24Ω.

A resistor is a passive two-terminal electrical component used in circuits to implement electrical resistance. Resistors have a variety of purposes in electronic circuits, including lowering current flow, adjusting signal levels, dividing voltages, biassing active components, and terminating transmission lines.

We are given that,

Voltage = δv =8v

Current = i =6a

So that , the resistance can be calculated by the formula by,

R = Vi

R = 8v × 6a

R = 24 Ω

Therefore , the of resistor would be 24Ω.

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The velocity of the baseball after it has been hit is 106.67 m/s and moving towards east.

Given that, impulse = 20 N/s

Mass m = 0.3 kg

Initial velocity of the baseball Vi = 40 m/s

We know the formula for impulse as change in momentum. It can be written as,

Impulse = m ( Vf - Vi)

20 = 0.3* (Vf - 40)

66.67 = -Vf - 40

Vf + 66.67 + 40 = 0

Vf = - 106.67 m/s

The velocity of the baseball after it has been hit is 106.67 m/s but in the opposite direction to the initial velocity direction of the ball.

Thus, the ball moves with 106.67 m/s towards east.

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If the darts are thrown at the same speed then (b) Projectile that travels along trajectory B was projected earlier and (c) Second dart must be projected at angle, such that 0 + 0,8 = 90° is correct.

Initial speed of dart A = u'

Angle of dart A = θ'

Initial speed of dart B = u''

Angle of dart B = θ''

The initial speed of both the darts is same,

Thus, u' = u'' = u

The darts are projected from same point A but not at same time; they are thrown one by one. But they travel same horizontal distance and reach B at the same time.

Since the horizontal range of both darts are same,

= [ u²sin(2θ') / g ] =  [ u²sin(2θ'') / g ]

= sin(2θ') = sin(2θ'')

Now, θ' is not equal to θ'', through the figure we can assume that θ'' > θ'

Since both are acute angles,

= sinθ'' > sinθ'

Multiplying both sides by 2u/g, we get,

= [ 2u X sinθ'' / g ] > [ 2u X sinθ' / g ]

which means, trajectory T of both the darts is as:

= T'' > T'.

Thus, statement B and C are correct options.

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The complete question:

A man wishes to throw two darts one by one at the target at B with same speed so that they arrive at the same time. Mark the correct statements about the two projections. Trajectory B Trajectory A А. B (A) Projectile that travels along trajectory A was projected earlier (B) Projectile that travels along trajectory B was projected earlier. (C) Second dart must be projected at angle e, such that 0 + 0,8 = 90° (D) Second dart must be projected at angle , >, STA​

If a neutron moves with a speed of 0.99c, its total energy is 1.07nJ, the rest energy is 0.15nJ , and kinetic energy is 0.92nJ

Given speed of neutron (v) = 0.99c

Mass of neutron = 1.674*10-27 kg

Total energy  = Rest energy +Kinetic energy

Let the Rest energy be E = mc^2

E = 1.674*10-27 kg x (3x10^8)^2 = 0.15nJ

E = 939.32MeV

Total energy (Er) = γmc^2

where γ = 1/√1-(v/c)^2

Er =  E/√1-(v/c)^2 = 939.32/√1-(0.99/3x10^8)^2

Er = 939.32/√1-0.9801 = 939.32/0.1411 = 6657.12MeV = 1.07nJ

Kinetic energy ( KE) = Total energy(Er) - rest energy(E)

KE = 1.07 - 0.15 =0.92nJ

Hence the rest energy of neutron is 0.15nJ while the total energy is 1.07nJ and kinetic energy is 0.92nJ

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Below is a list of the wavelengths in order of shortest to longest from left to right. Radiation comes in many different forms, including gamma rays, X-rays, UV, visible, infrared, microwaves, and radio waves.

The electromagnetic spectrum is made up of a wide variety of waves that are created when the electric field and magnetic field interact. It is believed that electromagnetic waves exhibit both wave and particle characteristics.

In essence, the photons—particle-like elements that make up electromagnetic waves and convey their energy, the wavelength and frequency of the waves. The class of electromagnetic waves is referred to as the "electromagnetic spectrum."

Electromagnetic waves are classified according to increasing wavelength: gamma rays, x-rays, ultraviolet, visible, infrared, microwaves, and radio waves.

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For each horizontal foot, the roller coaster changes 6 feet in height.

A roller coaster has a steep drop over a horizontal distance of 25 feet.

the distance is 25 ft.

At the bottom of the drop, the roller coaster is 150 feet tall. (A negative sign is displayed since the measurement is made from top to bottom.)

The increase is therefore 150 feet.

The roller coaster's gradient is,

m= rise/run= 150/25= 6

A slope of 6 indicates that the object rises by 6 units for every unit of run.

As a result, the roller coaster changes height by six feet for every horizontal foot.

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As per Torricelli's Theorem velocity of efflux, i.e., the velocity with which the liquid flows out of a hole is equal to [tex]\sqrt{2gh[/tex]

Where h = the depth of the hole below the liquid surface.

According to Bernoulli's principle, "Within a horizontal flow of fluid, points of higher fluid speed will have less pressure than points of slower fluid speed."

The more depth the hole is, the more the velocity of the liquid that comes out of the hole. The velocity is maximum if the hole is at the bottom of the tank.

Pipe velocity is an area-averaged property independent of the pipe's cross-sectional flow distribution. It does not matter whether the flow is laminar or turbulent. Along the central axis, fluid may be traveling at twice the calculated pipe velocity.

The given question is incomplete, the related concepts has been described  here for reference.

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The refrigerant trace gas that should be used to identify a leak is the HCFC-22. Nitrogen gas should also be used along with trace gas.

HCFC-22, also known as chlorodifluoromethane, is a colorless gas that is used as a propellant and refrigerant. It was the most commonly used refrigerant for air-conditioning systems in buildings, but if it leaks, it may cause ozone depletion. Nowadays, it is still used but only when recovered and recycled.

One use of HCFC-22 is to detect a leak in a system. To do that, the system is pressurized with a trace quantity of HCFC-22 to a certain pressure, then dry nitrogen is used to further increase the system pressure. The trace refrigerant is enough to be detected by a leak detector.

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An organiser of a bungee jumping competition changes the length of the bungee rope so different people can use the rope safely because high weight can cause the rope to stretch and break.

When a person jumps, their size impacts the bungee rope since their weight causes the rope to expand different manner. The force of a person's body weight causes the bungee rope to lengthen when they jump, and the degree of stretching depends on their mass. Since the force of the weight is greater, a bigger person will stretch the rope more than a lighter one. Due to this phenomenon, extra stretching of a rope can lead to breaking which can cause life hazards. Therefore, the organizer changes the length of the bungee rope.

For example, if an adult weighs twice as much as a kid, the bungee rope will stretch twice more than the kid's leaps. This is because the adult's weight is twice as much as the child's weight, so the force of the adult's weight will be twice as great, causing the rope to stretch twice as much.

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Answer: The answer is 120 Newton.

The rate of change of observer to rocket distance is 864 ft/sec when the rocket is 2400ft from the ground.

This question can be solved using the Pythagorean theorem.

Let us assume that:

the distance between the observer and launch pad be x.

the vertical distance of rocket and the launch pad (ground) be y.

As it is given in the question that this scenario forms a right angled triangle. So let the distance BC be r as shown in figure.

We have to find the value [tex]\frac{dr}{dt}[/tex]. (rate of change of distance r)

According to the question,

AB=x= 700 ft

AC=y= 2400 ft

[tex]\frac{dy}{dt} =900 ft/sec[/tex]

By Pythagorean theorem,

[tex]x^{2} +y^{2} =r^{2} (equation 1)\\r^{2} =700^{2} +2400^2\\r=2500 ft\\[/tex]

On differentiating equation 1 we get,

[tex]2r\frac{dr}{dt} =0+2y\frac{dy}{dt} \\r\frac{dr}{dt} =y\frac{dy}{dt}[/tex]

On putting the values and solving we get

[tex]\frac{dr}{dt} =864 ft/sec\\[/tex]

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The sun's brightness is not increasing, nor has the separation between it and Earth. The greater heat must result from the atmosphere's greenhouse gases absorbing more infrared energy.

A greenhouse gas, often known as a greenhouse gas (GHG or GhG), is a gas that produces the greenhouse effect by both absorbing and emitting radiant radiation in the thermal infrared range. Water vapour, carbon dioxide, methane, nitrous oxide, and ozone are the main greenhouse gases in the Earth's atmosphere (O3). Instead of the current average of 15 °C (59 °F), without greenhouse gases, the temperature of the Earth's surface would be closer to 18 °C (0 °F). Also containing greenhouse gases are the atmospheres of Venus, Mars, and Titan.

The amount of carbon dioxide in the atmosphere has grown by more than 50% due to human activity since the start of the Industrial Revolution (about 1750), rising from 280 parts per million in 1750 to 421 parts per million in 2022.

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The spring constant of the spring to which a block is attached and spring is compressed initially and then released is 16.67 N/m.

Energy is being transferred from one form to another form and follows conservation of energy.

Mathematically,

" 1/2 * k * x² = 1/2 * m * v² "

where, k is the spring constant = ?

Compression of the spring = 0.75 m

m is Mass of the block = 1.5 kg

v = velocity of the block = 2.5 m/s

Placing values in above equation, we get,

1/2* k * (0.75)² = 1/2* (1.5)* (2.5)²

k * (0.75)² = (1.5)* (2.5)²

k = [(1.5)* (2.5)²]/(0.75)² = 9.375/0.5625 = 16.67 N/m

Thus, the spring constant of the spring is 16.67 N/m.

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Nuclear fission reactions result in the release of kinetic energy.

What is nuclear fission ?

Nuclear fission is the procedure in nuclear physics whereby an atom's nucleus divides into two daughter cells

Nuclear fission is the process by which an atom's nucleus breaks into two lighter nuclei during a nuclear reaction. This decay may occur naturally as a result of spontaneous radioactive decay, or it may be replicated in a laboratory setting by meeting the appropriate circumstances (bombarding with neutrinos). The resultant fragments typically weigh less when combined than the initial bulk. In the aforementioned process, the missing mass is what is transformed into nuclear energy.The kinetic velocities of the neutrons and fission products make up the majority of the energy released. uranium-235, plutonium-239, a combination of the two typical of modern nuclear power reactors, and uranium-233 utilised in the thorium cycle thermal neutron fission product yields by mass.

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An automobile having tires with a 0.370-m radius may drive 80,000 km before needing new tires. The tires' total amount of revolutions over their lifetime is 3x10^7

Given that radius of tire = 0.370m

Distance the tire travels (s) = 80000km = 8 x 10^7 m

the number of rotations of the tire is = n

We know that circumference of tire = 2r = 1 revolution or rotation of tire

circumference = 2x3.14x0.370 = 2.32m per revolution

Number of revolutions made  = total distance / distance travelled in 1 revolution

n = 8 x 10^7/2.32 = 3.44 x 10^7

Hence number of revolutions made by the tire = 3 x 10^7

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The stage of life cycle of star in which hydrogen acts as the primary fuel for nuclear fusion is main sequence.

Nebulae, which are enormous clouds of gas and dust, are where all stars are born. Stars do not survive forever, despite the fact that they shine for tens of thousands or even millions of years. A star's size affects both its last phase of life and the changes that take place in it over time.

A star's energy comes from nuclear reactions at its core, which is why it shines so brightly. This phase is referred to as the "main sequence." A star's exact lifespan is highly dependent on its size. Massive stars quickly run out of fuel. They might only exist for a few hundred thousand years, then. Smaller stars burn up their fuel more gradually, lasting for several billion years.

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The coconut is subject to a downward force of 1.47 N from gravity. The gravitational pull of the tree causes a coconut to fall from it.

The gravitational pull is both an attracting and non-contact force. The coconut consequently falls from the tree. Given that palm trees may reach heights of up to 30 meters (98 feet) over, or the equivalent of an 8-story building, a coconut can fall at a rate of up to 85 kilometers per hour (53 mph). Accordingly, the force of the coconut as it lands on the ground is equal to a ton of weight.

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The main reason that the gravitational attraction between Earth and the Moon changes each day.

Option b is correct.

Tides are the result of the gravitational tug from the Moon and Sun that the Earth feels. If we disregard the Sun for now, the Earth's oceans facing the Moon bulge up in response to the lunar gravitational force: a high tide.

Even though the sun is much more massive and therefore has stronger overall gravity than the moon, the moon is closer to the earth so that its gravitational gradient is stronger than that of the sun.

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