. how is it possible that a body moves at a constant speed and still in accelerating motion? 2. when a car is going around a circular track with constant speed, what provides the centripetal force necessary for circular motion? 3. what are directions of acceleration and net force if the speed of an object is changing while rotating in a circular motion?

The speeds and the direction of each after the collision:

The proton = -1.692 x 10⁷m/s to the left.

The carbon = 0.3076 x 10⁷ m/s to the right.

If there are two object each with masses m₁ and m₂ move with speed v₁ and v₂, then the two objects collide, so after colliding the speed of each object becomes v₁’ and v₂'.

Since there are no external forces acting on the system, then the momentum of the system is conserved, meaning the momentum before and after the same collision.

The equation is:

(m₁)(v₁) + (m₂)(v₂) = (m₁v₁)' + (m₂v₂)'

We have,

velocity of the proton = 2.0 x 10⁷ m/s ⇒ v₁

Mass of the proton = m₁

The velocity of a carbon atom = 0 ⇒ v₂  

The mass of the carbon atom = 12 m₁

So, the speeds of proton after the collision:

(m₁)(v₁) + (m₂)(v₂) = (m₁v₁)' + (m₂v₂)'

v₁’ = (m₁ - m₂) / (m₁ + m₂) (v₁)

= (m₁ - 12m₁) / (m₁ + 12m₁) (2.0 x 10⁷)

= (-11 m₁) / (13m₁) (2.0 x 10⁷)

= -1.692 x 10⁷m/s ⇒ it's negative, so to the left.

Now, the speed of the carbon atom after collision:

V₂’ = (2m₁) / (m₁ + m₂)v₁

= 2/13 (2 x 10⁷)

=  0.3076 x 10⁷ m/s ⇒ it's positive, so to the right.

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The period of y for two satellites that are being watched as they orbit the planet is 22.63 times, and if the period of rotation of satellite x is T, satellite y.

Is four times as far from the Centre of the earth as satellite x. A satellite, often known as an artificial satellite, is a spacecraft that has been put into orbit on purpose. With the exception of passive satellites, most spacecraft have a method for producing electricity for the electronics they carry, such as solar cells or radioisotope thermoelectric generators. From above the Northern Hemisphere, Earth circles the Sun in a counterclockwise manner at an average distance of 149.60 million kilometres. It takes 365.256 days to complete one orbit.

Tx/Ty = (rx/ry) 3/2 = (8/1) 3/2 = 8 3/2 where Tx/Ty = (rx/ry) 3/2 =

X's revolution lasts for 8/3 = 22.63 times as long as Y does

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The effect is similar to a car colliding with a wall at a velocity  of 50 km/h.

The principle of conservation of linear momentum states that the sum of the initial momentum is equal to sum of the final momentum, provided that the system is Isolated.

Mathematically, the law of conservation of linear momentum is given as;

Pi = Pf

where;

m₁u₁ = m₂u₂

where;

Based on Newton's third law of motion, action and reaction are equal and opposite.

If the car collides with a stationary wall, the wall will exert equal and opposite reaction to the car. If a car hits a wall with a velocity of 50 km/h, the wall will move at a velocity of 50 km/h provided it has equal mass with the car.

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A body of mass 2.64 kg is pushed straight upward by a 32.9 N vertical force, then its acceleration is 2.67m/s^2

Given the mass of body (m) = 2.64kg

Force acting on the body (F) = 32.9N

We know that F = ma where a is the acceleration on the body.

Here when body is thrown upwards acceleration acts upwards along with the force but in the opposite direction the gravitational acceleration acts downwards.

Then Fg force due to gravity is = mg where g is the gravitational acceleration = 9.8m/s^2

Fnet = F - Fg

ma = F- mg

a = 32.9 - (2.64x9.8)/2.64 = 2.66

Hence the acceleration acting on the body is 2.67m/s^2

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A spectrum of seven colors ( red, orange, yellow, green, blue, indigo, and violet) is created when white light travels through a glass prism and is dispersed.

When white light travels through a prism, dispersion is the breaking of the light into its individual colors. The seven colors that make up the spectrum are produced. White light experiences varying degrees of color bending when it passes through a prism.

The longest wavelength and least bending color are red, yet violet bends the most. A red light would therefore be at the apex of the created spectrum, violet would be at the bottom, and the remaining hues or colors would be in between.

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The change in internal energy of system is −87 J and that of environment is 87 J.

Calculation :

given,

        Q = 164 j

        W = 77 j

Q = W +ΔU

77 = 164 + ΔU

ΔU = 77 - 164

      = - 87 j

The change in internal energy of system is −87 J and that of environment is 87 J.

In physics, energy is the quantitative property transmitted to the body or physical system, perceived in the performance of work and in the form of heat and light. Energy is Conserved - The law of conservation of energy states that energy can be transformed into form, but cannot be created or destroyed. The unit of measure for energy in the International System of Units (SI) is the joule (J).

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If the speed is doubled and the radius stays unchanged Acceleration becomes half.

For uniform circular motion, acceleration=v2/r where v is velocity and r is radius.

Let initial velocity be V and initial radius be R. So, initial acceleration = V2/R.

Finally, velocity is unchanged(=V) and radius is doubled. So, radius is 2R.

Hence, centripetal acceleration = V2/(2R) = 1/2 V2/R.

So, acceleration becomes half.

Any change in an object's velocity causes an acceleration, including increasing speed, decreasing speed, or changing direction. Yes, that's correct even when the traveling item neither speeds up nor slows down a change in direction of motion causes an acceleration.

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The maximum power that can be drawn from this photodiode is  5.6 μ w.

A photodiode is a light-touchy semiconductor diode. It produces cutting-edge when it absorbs photons. The bundle of a photodiode allows light to reach the sensitive part of the device. The bundle may additionally consist of lenses or optical filters.

Calculation:-

FF = Pmax/Pt

Pmax = ff× Pt

         = 0.5 * 80 μ * 140 m

        = Pmax = 5.6 μ w

Photodiodes. Photodiodes are a category of diodes that converts mild power to power. Their running is exactly the other of LEDs that are additionally diodes however they convert power to mild strength. Photodiodes also can be utilized in detecting the brightness of the light.

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a) The index of refraction for Jell-O is  1.027.

b) The angle of refraction is 38.28°.

The index of refraction measures how a light beam bends when it travels through different media. The refractive index n is defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction.

if i is the angle of incidence of a ray in vacuum (angle between the incoming ray and the perpendicular to the surface of a medium, known as the normal), and r is the angle of refraction (angle between the ray in the medium and the normal). Then:

[tex]n = \frac{sini}{sinr}[/tex]

a)   the index of refraction for Jell-O is = speed of light in air/speed of the light in the medium

=   3.00x 10^8 m/s /2.92 x 10^8 m/s

= 1.027

b) the angle of refraction is = sin⁻¹(1.027sin37.1°)

= 38.28°

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The potential (in v) of the power supply 6 Volt.

Calculation :

The energy formula ,

H = VIT

Where,

H=energy dissipated the lamp

I=current through the lamp

V = potential difference

t=time during which the current flows through the lamp

From the question we have,

Current(I)=0.3A

The Energy supplied(E)=216 j

Time during which the current flows(t)=2 minutes=2×60 seconds

H = VIT  

216 j = v * 0.3 A *120 sec

V = 216/( 0.3 A *120 sec)

V = 6 Volt

Scientists define energy as the ability to do work. Modern civilization is possible because humans have learned to convert energy from one form to another and use it for work.

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The distance from the hole must be 2.244 × 10⁻²⁷ m to detect a 1.0 cm diameter spread in the beam of pellets.

Given that,

Mass of the pellet m = 2 g

Speed of the pellet v = 120 m/s

Diameter of the hole d = 1.5 mm = 1.5 × 10⁻³ m

Distance between the pellet and the hole D = 1 cm = 1 × 10⁻² m

Let us find the wavelength,

λ = h/mv = (6.626 × 10⁻³⁶)/(2 × 120) = 2.76 × 10⁻³³ m

So, y = (1.22 λD)/d = (1.22 × 2.76 × 10⁻³³ × 1 × 10⁻²)/(1.5 × 10⁻³) = 2.244 × 10⁻²⁷ m

Thus, the distance from the hole must be 2.244 × 10⁻²⁷ m to detect a 1.0 cm diameter spread in the beam of pellets.

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The wavelength of an electromagnetic wave that has a frequency of 1 hertz  more than 1 m.

In a vacuum, electromagnetic waves move at a constant speed of 3.00 x 108 ms-1. Both the magnetic and electric fields have no effect on them. However, they can exhibit diffraction or interference. Any medium, including air, a solid, or a vacuum, can be traversed by an electromagnetic wave. It is not dependent on a medium to spread or move from one location to another. The opposite is true for mechanical waves, which require a medium to propagate (like sound or water waves). Transverse waves are electromagnetic waves. Thus, they are evaluated based on their amplitude (height) and wavelength (distance between the highest and lowest points of two successive waves).

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AutoLFADS is a framework for large-scale neural network training for generalised estimate of single-trial population dynamics.

What is neural network ?

Deep learning techniques are based on neural networks, sometimes referred to as artificial neural networks (ANNs) or simulated neural networks (SNNs), which are a subset of machine learning. Their structure and nomenclature are modelled after the human brain, mirroring the communication between organic neurons.

Deep neural network of population dynamics models require considerable hyperparameter adjustment for each dataset to function at the cutting edge. Without using behavioural or task information, AutoLFADS is a model-tuning framework that generates high-performing autoencoding models automatically using data from a range of brain regions and activities.

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The average rate of change in concentration is calculated to be 0.00404 M/s.

Average rate of change is described as (change in concentration)/(change in time).

Given the concentrations of the reactant (A), we may first determine the average change in A.

Change in A = 0.14 - 0.395 = -0.51 M

Average rate = -0.51 M/252 s = -0.00202 M/s

The negative sign indicates the decreasing [A] over time.

The stoichiometry of the equation, which states that two Bs are produced for every A utilised, is used to determine the average rate of change of B.

So, average rate of change of B is 2 × 0.00202 = 0.00404 M/s

The question is incomplete. The complete question is 'A → 2B

Time(s)      Concentration of A (M)

0.                0.65

126.             0.395

252.            0.140'

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Answer:To use these lenses to get the highest power telescopeFo=

Explanation:

The magnifier. Then we need only one lens. The angular exaggeration of the magnifier when the object is put veritably near to the focal point is given by the formula

M =

f

25 cm

where ff is the focal point. thus, the lower the focal length the larger the exaggeration therefore we should elect the lens with the shortest focal length which is the one with

f = 25 mm.

Step 2

2 of 4

{ The microscope.} The microscope. Then we need two lenses. The angular exaggeration of the microscope is given by

L ⋅ 25 cm

thus, lower the product of the focal lengths of the two lenses the larger the exaggeration. thus we should elect the two lenses with the lowest focal lengths i.e. boxed{f_0 = 25

= 25 mm and f

e

= 50 mm.

Step 3

3 of 4

{ The telescope.} The telescope. Then we need two lenses. The angular exaggeration of the telescope is given by

M = - frac{f_0}{f_e}

M = −

f

e

f

0

i.e. it's directly commensurable to the focal length of the objective lens and equally commensurable to the focal length of the eye piece lens. thus we should elect the objective lens with the loftiest possible focal length and the eyepiece lens with the lowest possible focal length

On a typical seismogram, surface waves will show the highest amplitudes.

Seismogram. the file of an earthquake's seismic waves produced through a seismograph. floor waves ( L ) remaining to go away focus; best travels via solids; reasons crust to ripple like waves on ocean (maximum destructive) Body waves ( P & S )waves journey quickest and are the primary to reach from the earthquake.

In S or shear waves, rock oscillates perpendicular to the course of wave propagation. In rock, S waves commonly journey approximately 60% the velocity of P waves, and the S wave constantly arrives after the P wave.

P waves are compressional waves and journey at the best velocity; hence, they come first.The primary, or P, waves journey maximum fast and are the primary to be registered through the seismograph. Secondary, or S, waves journey extra slowly.

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Answer:

32 A.

Explanation:

In a transformer, the ratio of the voltage across the primary coil to the voltage across the secondary coil is equal to the ratio of the current in the primary coil to the current in the secondary coil. This relationship is known as the transformer equation, and it can be written as follows:

Vp / Vs = Is / Ip

Where Vp is the voltage across the primary coil, Vs is the voltage across the secondary coil, Is is the current in the secondary coil, and Ip is the current in the primary coil.

Given the values provided in the problem, we can substitute them into the transformer equation to find the current in the primary coil:

Ip = (Vp * Is) / Vs

= (132 kV * 8 A) / 33 kV

= 32 A

Therefore, the current in the primary coil of the transformer is 32 A.

The energy in biomass is used to make electricity and the energy stored in biomass  in the form of chemical bonds.

Biomass contains stored chemical energy from sun and plants produce biomass through photosynthesis. Biomass can be burned directly for heat or converted to renewable liquid and gaseous fuels through various other processes. Biomass is organic, which means it is made up of material derived from living beings like plants or animals.

Biogas is obtained from organic wastes( animal excreta, agricultural waste etc.). These wastes have stored chemical energy in them, and these chemical energy convert into bio-energy on combustion.

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42 Hz is the frequency of a photon that is emitted when the dipole moment of a proton flips in a magnetic field of 2.1 t, the energy of a photon is related to its frequency by the equation e.

The magnetic influence on moving electric charges, electric currents and magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it when the charge is travelling through a magnetic field. The magnetic field of a permanent magnet pulls on ferromagnetic substances like iron and attracts or repels other magnets. Paramagnetism, diamagnetism, and antiferromagnetism are three additional magnetic effects that a nonuniform magnetic field can have on "nonmagnetic" materials, albeit these forces are often so minute that they can only be detected by laboratory equipment. Electric currents, like those utilized in electromagnets, and electric fields that change in time produce magnetic fields that surround magnetized things. Electric charges in motion and the intrinsic magnetic moments of elementary particles, which are connected to their spin, a fundamental quantum feature, create magnetic fields. As parts of the electromagnetic force, one of the four fundamental forces of nature, magnetic and electric fields are interdependent.

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Speed be after traveling 40 m is  10 m/s.

From kinetic equation we will have

[tex]Vf^{2}[/tex] - [tex]Vi^{2}[/tex] = 2ad

5² - Vi² = 2a × 10

after 40m distance

[tex]Vf^{2}[/tex] - [tex]Vi^{2}[/tex] = 2a × 40

here let say it start from rest

vi = 0

5² - 0 = 2a × 10

[tex]Vf^{2}[/tex] - 0  = 2a × 40

divide the two equation

[tex]Vf^{2}[/tex] /25 = 2a ×40 / 2a × 10

Vf  = 10 m/s

The rate at which an object moves in relation to a reference point is measured as its speed. It is regarded as a magnitude or scalar quantity and has no direction. The formula: can be used to calculate speed.

Speed equals Distance/Time.

Average Speed - The average speed of an object is determined by the distance it covered in a predetermined amount of time. A car's average speed over the period of an hour if it traveled 50 miles is 50 mph. The car may have experienced instantaneous speeds between 40 and 60 mph throughout that time, but its average speed was 50 mph.

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We will connect 18 resistors in series and in this combination we will get 3.5V across the last 7 resistors.

     _________R1__________R2________

as shown above let R1 and R2 be the final combination of resistors and the voltage across R2 be 3.5V

  since the combination is connected across 9V battery so we need to find the current flown through the circuit.

let the current through the circuit be I

so I = [tex]\frac{9}{R_1+R_2}[/tex]

so the voltage across R2  is  R2 *i

and  we have assumed that the volatage across R is 3.5V.

so 3.5 = (9*R2)/(R1+R2)

=>   3.5R1+ 3.5R2 =9R2

=>   3.5R1 = 5.5R2

=>    7R1 = 11 R2

so R1= 11Ω and R2 = 7Ω

so we have a series combination of 18 resistors and voltage across the last 7 resistor is 3.5V

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The car will be going with the speed of 20m/s in 5 seconds.

It is provided that a car is starting from the rest and has a constant acceleration of 4m/s².

The time taken by the car during its motion is 5 seconds.

Using the first equation of motion,

V = U+at

Where,

V is the final velocity,

U is the initial velocity

a is the acceleration and,

t is the time taken by the car during the motion.

Now, putting all the values accordingly,

V = 4 × 5

V = 20 m/s.

So, the car will be going at a speed of 20m/s in 5 seconds.

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After separation, each sphere will have a charge of 250e, which is equal to the total excess charge that was transferred between the two spheres.

After sphere x loses 500 electrons, it becomes negatively charged, with a charge of -500e, where e is the charge on an electron. After sphere y gains 1000 electrons, it becomes positively charged, with a charge of 1000e.

When the two spheres are put in contact with each other and then separated, they will transfer some of their excess charges to each other until they are both neutralized. This means that sphere x will lose some of its excess electrons to sphere y, and sphere y will gain some of the electrons that sphere x loses.

The total charge of the two spheres after separation will be the sum of the charges on each sphere. Therefore, the charge on sphere x after separation will be (-500e + 1000e) / 2 = 250e, and the charge on sphere y after separation will be (-500e + 1000e) / 2 = 250e.

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The diameter of the lowest string is = 4 x the diameter of the highest string.

Option ( B ) is correct.

According to the given data in the question,

The number of strings on the guitar = 6

The highest string is vibrating 4 times more than that the lowest string.

The formula of the frequency is shown as,

[tex]F = \frac{V}{2L}[/tex]

V = velocity of the sound

L = length of the string

The formula of frequency could also be written as -

u is the linear density of the string ⇒ u = m / L

m is the mass of the string

T is the tension of the string,

[tex]F = \frac{1}{2L}\sqrt \frac{T}{u}[/tex]

A is depicted as the cross-sectional area of the string and d is the diameter so the mass =

m = ρ x A x L (ρ is the density)

m = ρ x [tex]\frac{\pi }{4}[/tex] x [tex]d^{2}[/tex] x L

Frequency =

[tex]F = \frac{1}{2L}\sqrt \frac{T}{u}[/tex]

F = [tex]\frac{1}{2L}[/tex] x [tex]\sqrt{} \frac{4T}{p\pi d^{2} }[/tex]

F = [tex]\frac{1}{L}\frac{1}{d}\sqrt{}\frac{4T}{p\pi }[/tex]

Lengths of the string are the same so frequency is inversely proportional to string diameter,

F ∝ [tex]\frac{1}{d}[/tex]

So, 4F( low ) = F ( high )

d ( low ) = 4d ( high )

Therefore, The diameter of the lowest string is = 4 x the diameter of the highest string.

Option ( B ) is correct.

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The 6 strings on a guitar all have about the same length and are stretched with about the same tension.The highest string vibrates with a frequency that is 4 times that of the lowest string.

If the strings are made of the same material, how would you expect the diameters of the lowest and highest strings to compare?

A. d(low)=2d(high)

B. d(low)=4d(high)

C. d(low)=16d(high)

Answer: v = 1.64 m/s

Explanation:

Fc = (m * v^2)/r

v = [tex]\sqrt{(r * Fc) / m}[/tex]

v = sqrt((1.31m * (30.2 N - (2.55kg * 9.8 m/s^2))) / 2.55 kg)

v = 1.64 m/s

A mass m object travels along a circular path with a radius r at a constant speed v. The object is subjected to a net force of f. The mass stays unchanged if the object's acceleration is cut in half.

An item moving in a circle at a consistent speed is known as uniform circular motion. An object constantly changes its direction as it moves in a circle. The object is always traveling tangent to the circle.

Given that an object experiences centripetal force as it moves in a circular motion.

So, Force (f) is = mv2/r, where m is an object's mass, v is its speed, and r is its path's radius.

In this case, centripetal acceleration is equal to (ac) = v2/r.

Given that when acceleration is halved:

ac' = ac/2 = v^2/2r

There is no effect on mass as it will remain constant throughout the circular motion of the object but net force will be effected.

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The true statement of the magnitudes of tensions T₁, T2, and T3 in the

ropes in the diagram shown is the sum of the y-components of T₁ and

T₂ is equal to 20 N.

Option C is correct.

Tension is described as the pulling force transmitted axially by the means of a string, a rope, chain, or similar object, or by each end of a rod, truss member, or similar three-dimensional object.

Tension might also be described as the action-reaction pair of forces acting at each end of said elements.

We know that the block remains in equilibrium, so the forces must balance themselves in each direction at all points.

Consider the forces acting at the intersection of the three strings.

Here T3 =W=20N

The forces at the point must balance in vertical direction.

Therefore T3= Sum of y-components of T1 and T2 =20N

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The tennis ball is 2.15 metre above the court.

The tennis ball departs from the racket horizontally with a speed of 29m/s and it hits the court at a horizontal distance of 19.3 m from the racket.

The vertical height of the tennis ball before it leave the racket can be found by using the relation,

R = V√(2H/g)

Where,

R is the horizontal range,

V is the initial speed of the tennis ball,

H is the vertical height of the tennis ball from the court,

g is the gravitational acceleration.

Putting all the values,

We get,

19.3 = 29√(2H/9.8)

H = 2.15 m.

So, the height of the tennis ball is 2.15m

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