You observe a spiral galaxy with a large central bulge and tightly wrapped arms. It would be classified a

Answer: The global warming is affecting even the most cold places on earth, where we can find the polar ice caps and the glaciers. These places belong to the arctic glacial ocean.

Explanation: In the pass of time, due the human action on the enviroment, the desappear of the polar ice cover are increasing day after day. We, people, are loosing the prime earth air condicioner sistem, which helps to regulate the climate sistem since the entire history of humanity.

In the year of 2018, researches estimated that the total volume of Arctic sea ice in late summer declined, by two estimates, by 75 percent in half a century.

We must know that the decrease of the arctic sea ice have deep effects on the climactic sistem of earth and, considering the polar ice caps desappearence, the sea temperature will increase a lot, due the reflection of ultraviolet rays on the blue ocean, (not anymore on the white ice), transforming what should be the earth air condicioner sistem to a strong heater.

Answer:

Option A

Explanation:

Immediate corrective measure happens at the instant as it triggers a reaction according to a particular situation.

The time period of the solution is also on the same pattern and is not sustainable.

Thus the case where the stamping machine malfunctions and there is immediate removal of the machine from the service in order to reduce the production of the defective components is an example of immediate corrective measure.

Answer:

100 N

Explanation:

Let us first find the mass of the person when they are on the earth's surface

[tex]F=G\frac{Mm}{r^{2} }\\[/tex]

Now let us see how F changes if the distance between two masses is doubled

[tex]F_{1}  = G\frac{Mm}{(2r)^{2} } = \frac{1}{4} *G\frac{Mm}{r^{2} }[/tex]

So when the distance of separation is doubled, the force of gravity between the two masses decreases by a factor of four

Therefore her new weight = 400 N/4 = 100 N

Final answer:

The weight of the weight watcher on top of the tall ladder would be 1/4 of her normal weight due to the decrease in gravity with distance from Earth's center.

Explanation:

The weight of the weight watcher on top of a very tall ladder, twice her normal distance from Earth's center, would be 1/4 of her normal weight. This is because the gravitational force decreases with distance from the center of the Earth. When experiencing 1/4 the normal gravitational force, her weight would be 1/4 of the original weight.

Answer:

a. True

Explanation:

Pressure is always inversely proportional to the cross section area

This can be proven from the equation P = F/A

Where P = Pressure, F = Force and A = Cross-sectional area

This can also be similarly proven from the continuity equation given as

A₁V₁ = A₂V₂

Where A₁ = Area in first part of pipe (point A)

A₂ = Area in second part of pipe (point B)

V₁ = Velocity of water in first part of pipe (point A)

V₂ = Velocity of water in second part of pipe (point B)

From the continuity equation we can have that

V₁/V₂ = A₂/A₁

Thus the velocity of the liquid at any point in the pipe is inversely proportional to the cross-sectional area of the pipe. The liquid will be moving  slowly where the area is large and will be moving rapidly where the area  is small, and since the velocity is directly proportional to the force (F = m × v/t)which id in turn directly proportional to the pressure (P = F/A), this proves my answer to be True!

Answer:

False

Explanation:

We know that if path difference is even multiple of wavelength then bright fringes are formed and if path difference is odd multiple of wavelength then dark fringes are formed .

For bright fringes

Path difference Δx = m λ

m = 0 , 2 , 4 , 6.......

If m = 2 then the path difference will be

Δx = 2 λ

therefore the above statement if false.

False

You are travelling on a narrow two-lane road and are approaching a child riding his bike on the right side of the road. A line of oncoming vehicles following a slow moving truck is approaching in the oncoming lane. You should flash your lights and tap your horn and: slow down and move closer to the truck

Explanation:

Change just a single lane at once. While switching to another lane to get ready for a turn, you should flag your goal to do as such at any rate 200 feet preceding evolving lanes or turning. Your sign separation must be in any event 300 feet before the turn in the event that you are working a vehicle in a speed zone of at any rate 50 miles for every hour.

Try not to zigzag all around lanes, which will significantly build your hazard of a mishap. On the thru-way, more slow vehicles should utilise the correct lane. Leave the left-hand lane for quicker moving or passing vehicles. Keep below principles when you are moving to another lane:  

You should slow down and prepare to stop if necessary, yielding to the child on the bike. Flashing lights and honking the horn are not substitutes for cautious driving. Obey local traffic laws and be patient until it is safe to pass.

You are traveling on a narrow two-lane road and are approaching a child riding his bike on the right side of the road. A line of oncoming vehicles following a slow moving truck is approaching in the oncoming lane. To ensure safety, it's crucial not to rely solely on flashing your lights or tapping your horn. Your primary focus should be on slowing down and preparing to stop if necessary to yield to the child on the bike. Remember, flashing lights and using your horn can alert others, but they are not substitute for cautious driving. It's vital to exercise patience and wait until the oncoming traffic has passed and it is safe to overtake the child with a safe distance. Additionally, as a part of traffic safety, always be aware of and obey local laws regarding passing school buses with flashing lights, driving in school zones, and the general requirement to drive on the right hand side when encountering oncoming traffic.

Final answer:

The colorful effects seen when gasoline creates a thin film on water are a demonstration of thin-film interference, due to light waves reflecting and interfering from the surfaces of the film. The phenomenon causes different colors to appear based on the film's thickness and the light's wavelength.

Explanation:

The colors seen when gasoline forms a thin film on water are due to thin-film interference. This optical phenomenon occurs when light waves reflected from the top and bottom surfaces of a thin film, such as oil or a soap bubble, combine. The interference can be constructive or destructive, depending on the phase difference between the waves. Constructive interference results in bright colors, while destructive interference can cause darkness or cancellation of color. The film's varying thickness results in different colors because each color in the visible spectrum has a different wavelength; thinner or thicker areas interfere with different colors differently.

Early experiments in this area by Agnes Pockels helped to lay the groundwork for our understanding of thin films. Interference effects are most noticeable when light interacts with objects that have sizes similar to the wavelength of light, a principle that is also applied in designing anti-reflection coatings and optical filters.

Final answer:

The colorful effects seen when gasoline or oil creates a thin layer on water are due to thin-film interference, a result of constructive interference of light reflecting off the film's surfaces.

Explanation:

The colors seen when gasoline forms a thin film on water are a demonstration of thin-film interference. This occurs due to the interference of light that is reflected off different surfaces of a thin film such as oil or a soap bubble. The phenomenon is explained by the wave nature of light, which when interacting with objects similar in size to its wavelength, causes some wavelengths of light to interfere constructively, creating bright and vivid colors. The observed colors vary because the thickness of the film affects which wavelengths interfere constructively.

Historical contributions to the study of thin-film interference include the work of Agnes Pockels. She developed a trough for measuring surface films, aiding in the investigation of these colorful effects. Moreover, commercial applications like anti-reflection coatings and optical filters utilize thin film interference principles for effectiveness.

Answer:

#4 Electrical energy to thermal energy

Explanation:

You clue there is constant speed, this means that the lift is not accelerating. So if that is the case, the lift is experiencing a resistive force against gravity. The one doing exerting the resistive force is the motor, which runs on electrical energy. Resistive force transforms into heat, so that makes it thermal energy. And so, the answer would be the last case.

Answer:

Amplitude of the resultant wave = 15.72 cm

Explanation:

If two identical waves are traveling in the same direction, with the same frequency, wavelength and amplitude; BUT differ in phase the waves add together.    

A = 9cm (amplitude)

φ = 45 (phase angle)

The two waves are y1 and y2

y =  y1 + y2

where y1 = 9 sin (kx - ωt)    

and   y2 = 9 sin (kx - ωt + 45)

y       = 9 sin(kx - ωt) + 9 sin(kx - ωt + 45)  =  9  sin (a)   +   9  sin (b)

where a =  (kx - ωt)

abd b = (kx - ωt + 45)

Apply trig identity: sin a + sin b = 2 cos((a-b)/2) sin((a+b)/2)

A  sin (   a    )   +   A  sin (     b    ) = 2A cos((a-b)/2) sin((a+b)/2)

We have that

9  sin (   a    )   +   9  sin (     b    ) = 2(9) cos((a-b)/2) sin((a+b)/2)

= 2(9) cos[(kx - wt -(kx - wt + 45))/2] sin[(kx - wt +(kx -wt +45)/2]

y       = 2(9) cos (φ /2) sin (kx - ωt + 45/2)

The resultant sinusoidal wave has the same frequency and wavelength as the original waves, but the amplitude has changed:  

Amplitude equals 2(9) cos (45/2) = 18 cos (22.5°) = 18 * -0.87330464009

= -15.7194835217 cm ≅ 15.72 cm

since amplitudes cannot be negative our answer is 15.72 cm

Answer:

Force constant will be 1195.85 N/m

Work done will be 1.6859 J

Explanation:

We have given the force,  F = 63.5 N

Spring is stretched by 5.31 cm

So x = 0.0531 m

Force is given , F = 63.5 N

We know that force is given by [tex]F=kx[/tex]

So [tex]63.5=k\times 0.0531[/tex]

k = 1195.85 N/m

Now we have to find the work done

We know that work done is given by

[tex]W=\frac{1}{2}kx^2=\frac{1}{2}\times 1195.85\times 0.0531^2=1.6859J[/tex]

Answer:13.33 tons

Explanation:

Given

Weight of a material varies as

[tex]W\propto b[/tex]  (width)

[tex]W\propto h^2[/tex]  (height)

[tex]W\propto \frac{1}{L}[/tex]  (length)

[tex]W=k\frac{bh^2}{L}[/tex]

Dimension of first beam

[tex]b=\frac{1}{3}[/tex] foot

[tex]h=\frac{1}{2}[/tex] foot

[tex]L=15[/tex] foot

Weight supported [tex]W=20 tons[/tex]

Second beam

[tex]b=\frac{1}{2} foot[/tex]

[tex]h=\frac{1}{3} foot[/tex]

[tex]h=15 feet[/tex]

let weight of second beam be [tex]W_2[/tex]

taking both beams at the same time

[tex]\frac{20}{W_2}=\frac{\frac{1}{3}\times (\frac{1}{2})^2}{15}\times \frac{15}{\frac{1}{2}\times (\frac{1}{3})^2}[/tex]

[tex]\frac{20}{W_2}=\frac{3}{2}[/tex]

[tex]W_2=\frac{40}{3} \approx 13.33 tons[/tex]

Answer:

(C) both tech A and tech B

Explanation:

both technicians are correct because an accident could cause faults due to hidden damages which might not have been detected at the time of the accident and some faults could be related to previous repair probable due to human error from the repair man or even improper repair due to lack of adequate knowledge on the vehicle.

Answer:

Work done will be 22216.894 J

Explanation:

We have given mass of the skier m = 71 kg

Acceleration due to gravity [tex]g=9.8m/sec^2[/tex]

Slop is given as [tex]\Theta =31^{\circ}[/tex]

Distance d = 62 m

So vertical distance [tex]d_y=dsin\Theta =62\times sin31^{\circ}=31.932m[/tex]

We know that work done is given by

[tex]W=mgh=mgd_y=71\times 9.8\times 31.93=22216.894J[/tex]

Answer:

A perfect example of wave reflection is an echo.

Explanation:

A wave reflection takes place when waves cannot pass through a surface and in turn they bounce back. It is not necessary that wave reflections can only happen with sound waves, they can also take place in light waves. Also, the waves which are reflected have the same frequency as the original wave, but their direction is different. When a wave strikes an object in the same angle, they bounce back straight but when they hit an object with different angle, their direction changes.

The rollercoaster initially had 78,000 J of energy. It converted two-thirds of the energy into kinetic energy and later doubled it on a curve. Therefore, the coaster's new total mechanical energy is 182,000 J.

In this energy problem, the roller coaster car starts out with 78,000 J of potential energy. It then converts two-thirds of its energy into kinetic energy, which is 2/3 * 78,000 J = 52,000 J. However, this isn't the end of the energy conversion. As the roller coaster car takes a curve, it doubles its kinetic energy to become 2 * 52,000 J = 104,000 J. Therefore, the new total mechanical energy of the car, considering both its remaining potential and newly gained kinetic energy, is its original potential energy (78,000 J) minus the potential energy converted to kinetic and then doubled (2/3 * 78,000 J * 2), which gives us 78,000 J - (2/3 * 78,000 J * 2) = 78,000 J - 104,000 J = -26,000 J. However, energy can't be negative, so it means the question might be flawed or we need to ignore the energy conservation law in this case and simply sum up potential and kinetic energies getting 78,000 J + 104,000 J = 182,000 J.

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To find the mechanical energy of the roller coaster car, we calculate the converted kinetic energy and then account for it being doubled during the ride. The car's total mechanical energy remains at 78,000 J due to conservation of energy.

The problem involves calculating the mechanical energy of a roller coaster car after it has converted some of its initial potential energy into kinetic energy and then doubled that kinetic energy. Initially, the car starts with 78,000 J of potential energy. As the problem states, the car converts two-thirds of this energy into kinetic energy. This conversion can be calculated as (2/3) × 78,000 J = 52,000 J of kinetic energy. Then, as the car takes a curve, it doubles this kinetic energy, resulting in 2 × 52,000 J = 104,000 J of kinetic energy. Due to the conservation of mechanical energy, and considering that no energy is lost to friction or other forces, the total mechanical energy of the car will be the same as the initial potential energy it had at the top of the first rise. Therefore, the car now has a total mechanical energy of 78,000 J.

Answer:

405.3m

Explanation:

Since the CD spin rate is 500 rpm, or revolution per minutes, its angular speed in rad per second is

[tex]\omega = 500 rev/min * 2\pi rad/rev * 1/60 min/sec = 52.36 rad/s[/tex]

The dusk is 4.3 cm from center, so its velocity must be

[tex]v = R\omega = 4.3 * 52.36 = 225.14 cm/s[/tex]

Then the distance traveled by the dusk after 3 minutes, or 180 seconds is

[tex]d = v*t = 225.14 * 180 = 40526.54 cm[/tex] or 405.3m

By using the concepts of the Photoelectric effect, the wavelength of the light beam incident on a barium target with a work function of 2.50 eV and requiring a potential difference of 1.00V to turn back all the ejected electrons is calculated to be 355 nm.

To answer this question, we need to utilize the Photoelectric effect, which explains the relation between light and electrons. It determines the minimum amount of energy that a particle of light, a photon, must possess to eject an electron from a material, which is called the work function. In this case, the work function (W) of the barium target is given as 2.50 eV.

But we also need to account for the potential difference of 1.00V required to turn back the electrons. When 1 eV is required to turn back the electrons, it implies that the electrons have an extra energy value of 1 eV after overcoming the work function. We can combine these energies to find the total energy of the light beam as W + 1.00 eV which gives us 3.50 eV.

Now, we convert the total energy of the light beam from electronvolts to joules by multiplying with a conversion factor of 1.6 x 10^-19 J/eV. Therefore, we get E = 3.50 eV x 1.6 x 10^-19 J/eV = 5.6 x 10^-19 J.

We can then find the frequency of the light beam using the equation E = hv, where h is Planck’s constant (6.63 x 10^-34 Js) and v is the frequency. So, v = E / h = (5.6 x 10^-19 J) / (6.63 x 10^-34 Js) = 8.44 x 10^14 Hz.

Finally, we calculate the wavelength using the equation c = λv, where c is the speed of light (3 x10^8 m/s), λ is the wavelength, and v is the frequency. So, λ = c / v = (3 x 10^8 m/s) / (8.44 x 10^14 Hz) = 3.55 x 10^-7 m or 355 nm.

Therefore, the wavelength of the light beam is 355 nm.

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Answer:

The angular speed is 0.83 rad/s.

Explanation:

Given that,

Mass of disk M=49 kg

Radius = 1.7 m

Mass of child m= 29 kg

Speed = 2.6 m/s

Suppose if the disk was initially at rest , now how fast is it rotating

We need to calculate the angular speed

Using conservation of momentum

[tex]m\omega_{i}=(mr^2+\dfrac{Mr^2}{2})\omega_{f}[/tex]

[tex]mvR=(mr^2+\dfrac{Mr^2}{2})\omega[/tex]

Put the value into the formula

[tex]29\times2.6\times1.7=(29\times1.7^2+\dfrac{49\times1.7^2}{2})\omega_{f}[/tex]

[tex]\omega_{f}=\dfrac{29\times2.6\times1.7}{(29\times1.7^2+\dfrac{49\times1.7^2}{2})}[/tex]

[tex]\omega_{f}=0.83\ rad/s[/tex]

Hence, The angular speed is 0.83 rad/s.

The angular speed is mathematically given as

wf=0.83rad/s

Question Parameter(s):

Generally, the equation for the conservation of momentum   is mathematically given as

[tex]m\omega_{i}=(mr^2+\frac{Mr^2}{2})\omega_{f}[/tex]

Therefore

[tex]29\*2.6*1.7=(29\times1.7^2+\frac{49*1.7^2}{2})\omega_{f}[/tex]

wf=0.83rad/s

In conclusion, the angular speed is

wf=0.83rad/s

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Answer:

Probability of tunneling is [tex]10^{- 1.17\times 10^{32}}[/tex]

Solution:

As per the question:

Velocity of the tennis ball, v = 120 mph = 54 m/s

Mass of the tennis ball, m = 100 g = 0.1 kg

Thickness of the tennis ball, t = 2.0 mm = [tex]2.0\times 10^{- 3}\ m[/tex]

Max velocity of the tennis ball, [tex]v_{m} = 200\ mph[/tex] = 89 m/s

Now,

The maximum kinetic energy of the tennis ball is given by:

[tex]KE = \frac{1}{2}mv_{m}^{2} = \frac{1}{2}\times 0.1\times 89^{2} = 396.05\ J[/tex]

Kinetic energy of the tennis ball, KE' = [tex]\frac{1}{2}mv^{2} = 0.5\times 0.1\times 54^{2} = 154.8\ m/s[/tex]

Now, the distance the ball can penetrate to is given by:

[tex]\eta = \frac{\bar{h}}{\sqrt{2m(KE - KE')}}[/tex]

[tex]\bar{h} = \frac{h}{2\pi} = \frac{6.626\times 10^{- 34}}{2\pi} = 1.0545\times 10^{- 34}\ Js[/tex]

Thus

[tex]\eta = \frac{1.0545\times 10^{- 34}}{\sqrt{2\times 0.1(396.05 - 154.8)}}[/tex]

[tex]\eta = \frac{1.0545\times 10^{- 34}}{\sqrt{2\times 0.1(396.05 - 154.8)}}[/tex]

[tex]\eta = 1.52\times 10^{-35}\ m[/tex]

Now,

We can calculate the tunneling probability as:

[tex]P(t) = e^{\frac{- 2t}{\eta}}[/tex]

[tex]P(t) = e^{\frac{- 2\times 2.0\times 10^{- 3}}{1.52\times 10^{-35}}} = e^{-2.63\times 10^{32}}[/tex]

[tex]P(t) = e^{-2.63\times 10^{32}}[/tex]

Taking log on both the sides:

[tex]logP(t) = -2.63\times 10^{32} loge[/tex]

[tex]P(t) = 10^{- 1.17\times 10^{32}}[/tex]

The acceleration of the cart is 7.14 m/s^2. The tension in the string between the pulley and the cart is approximately 2.26 N.

This physics problem involves the principles of dynamics and rotational motion.

(a) First, using Newton's second law, the acceleration a of the cart (mass, m) pulled by a force F is given by a = F/m. So, the acceleration is a = 2.50 N / 0.350 kg = 7.14 m/s^2.

(b) Considering the pulley, the torque τ exerted by the tension in the string is τ = r * T, r being the radius of the pulley. Given that τ = I * α and α = a/r (α being the angular acceleration), we can express the tension T as T = (I * a)/(r^2) = (6.00 × 10^-6 kg*m^2 * 7.14 m/s^2) / (0.0135 m)^2 = approximately 2.26 N.

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Answer:

4.53 hours

Explanation:

Energy, E = 98000 J

Voltage, V = 3 V

Current, i = 2 A

Let t be the time for which the batteries give the power.

Energy = V x i x t

98000 = 3 x 2 x t

t = 16333.33 seconds

t = 4.53 hours

Considering the gasses law and all the parameters, 1) the pressure inside the cylinder is 3249.4 Pa, 2) the height of the piston at 18ºC is 0.4452 m.

The law of gasses is a group of chemical and physical laws that allows understanding the behavior of gasses in a close system.

The law of gasses considers different parameters, such as

When talking about standard conditions in gas, we refer to 1 atm pressure, 273 K of temperature (0ºC), and 22.4 L/mol of volume.

The different laws are,

The relationship between these three laws and the variables is as follows,

                                 (P₁V₁) / T₁ = (P₂V₂) / T₂

According to this framework, we can answer the questions in this porblem.

Available data:

A) What is the gas pressure inside the cylinder?

We know that P is defined by the relationship between force and area.

P = F/A

So, let us define Force and Area.

F is the force applied by the piston. So we need to get the F of the piston.

To do it, we will use the following formula,

 W = mg             ⇒  Where m is mass (15 kg) and g is gravity (9.8m/s²)

Since W is a type of force, we can replace this value in the previous general formula,

P = F/A = W/A = mg/A

Area A is defined by the following formula

A = π r²

Where

- π = 3.1416

- r = D/2

Now, we can replace A in the general formula as follows,

P = mg/A = mg / π (D/2)²

The pressure inside the cylinder is,

P = mg / π (D/2)²

P = (15 x 9.8) / 3.1416 (12)²

P = 147 / 452.39

P = 0.32494

P = 3249.4 Pa

The gas pressure inside the cylinder 3249.4 Pa.

B) What will the height of the piston be if the temperature is lowered to 18 ∘C?

T₁ = 588 K

T₂ = 18 ºC ⇒ 18 + 273 = 291 K

Now, volume can be calculated as follows,

V = π r² h = A h

Where

- π = 3.1416

- r = D/2 = 12

- h₁ = 0.9 m

- A = 452.39 cm² = 0.4524 m²

Replacing,

V₁ = A h₁

V₁ = 0.4524 m² x  0.9 m

V₁ = 0.4071 m³

Now, we have the initial volume V₁, and the inicial and final temperatures, T₁ and T₂. We will use this values and the Charles law to get the final volume, V₂.

V₁/T₁ = V₂/T₂

V₂ = T₂ (V₁/T₁)

V₂ = 291 (0.4071/588)

V₂ = 291 (0.4071/588)

V₂ =0.2014

Now that we have the final volume, we can use this value to get the final height.

V₂ = A h₂

h = V₂/A

h₂ = 0.2014 m³ / 0.4524 m²

h₂ = 0.4452 m

The height of the piston when the temperature is lowered to 18ºC is 0.4452 m.

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Final answer:

Starting with Part A, the gas pressure inside the cylinder is calculated using the piston's weight and area of the cylinder's cross-section, plus atmospheric pressure. For Part B, the height of the piston at 18 °C is found using the combined gas law, with the final volume corresponding to the new height under constant pressure.

Explanation:

To answer the student's questions regarding the cylinder and piston system, we must use the principles of gas laws and mechanics.

Part A: Gas Pressure Inside the Cylinder

The pressure exerted by the piston onto the gas can be calculated using the formula P = F/A, where F is the force and A is the area. The force due to the piston's weight (F) is the mass of the piston times the gravitational acceleration (F = m * g). The area (A) is the cross-sectional area of the cylinder, which is πr² for a circle. Adding the atmospheric pressure above the piston gives us the total pressure exerted on the gas inside the cylinder.

Part B: Height of the Piston at 18 °C

Assuming the process is isobaric (constant pressure), the change in height can be found using the combined gas law which relates pressure, volume, and temperature of a gas. In this case, P1V1/T1 = P2V2/T2, where V1 and V2 are the initial and final volumes, respectively, determined by the product of the cross-sectional area and the height of the piston, P is pressure, and T is temperature in Kelvin. We are looking for the final volume, and thus the final height of the piston when the temperature is lowered.

Answer:

1.556 N , 0.989 N, 0.567 N

Explanation:

Radius of sphere, r = 1.21 cm = 0.0121 m

density of platinum , d = 2.14 x 10^4 kg/m^3

density of mercury, d' = 13.6 x 10^3 kg/m^3

Volume of sphere, [tex]\frac{4}{3}\pi \times r^{3}= \frac{4}{3}\times 1.34\times \left (0.0121  \right )^{3}[/tex]

V = 7.42 x 10^-6 m^3

Weight of sphere = volume of sphere x density of platinum x gravity

W = V x d x g = 7.42 x 10^-6 x 2.14 x 10^4 x 9.8 = 1.556 N

Buoyant force, B = Volume x density of mercury x gravity

B = 7.42 x 10^-6 x 13.6 x 10^3 x 9.8 = 0.989 N

Apparent weight = True weight - Buoyant force

Apparent weight = 1.556 - 0.989 = 0.567 N

To find the weight of the platinum sphere, calculate the mass of the sphere using its density and volume. Then, use the formula weight = mass × gravitational acceleration. The buoyant force acting on the sphere is equal to the weight of the fluid displaced, which in this case is the weight of an equivalent volume of mercury. The sphere's apparent weight can be calculated by subtracting the buoyant force from its actual weight.

To find the weight of the platinum sphere, we can use the formula:

Weight = Mass × Gravitational acceleration

Given the density of platinum and the radius of the sphere, we can calculate the mass of the sphere using the formula:

Mass = Density × Volume

Using the volume of a sphere formula, we can determine the volume of the sphere. Once we have the mass, we can calculate the weight of the sphere.

The buoyant force acting on the sphere can be calculated using Archimedes' principle, which states that the buoyant force equals the weight of the fluid displaced. In this case, the fluid is mercury. Since the sphere is totally immersed in mercury, the buoyant force would be the weight of an equivalent volume of mercury.

The sphere's apparent weight can be calculated by subtracting the buoyant force from the weight of the sphere. This gives us the net force acting on the sphere when it is immersed in mercury.

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Answer:

[tex]\mu_s=1.0205[/tex]

Explanation:

Given:

For the condition of no slip the force of  static friction must be greater than the applied force so that there is no skidding between the contact surfaces at the contact point.

[tex]\therefore F<f_s[/tex]

where:

[tex]f_s[/tex] = static frictional force

[tex]\Rightarrow 20<\mu_s\times N[/tex]

[tex]\Rightarrow 20<\mu_s\times m.g[/tex]

[tex]\Rightarrow 20<\mu_s\times 2\times 9.8[/tex]

[tex]\mu_s>1.0204[/tex]

Answer:

2388078.86544 N/C

Explanation:

[tex]\rho[/tex] = Charge density = 9.22 mC/m³

r = Distance = 7.35 cm

[tex]r_o[/tex] = Outer radius = 3.5 cm

[tex]r_i[/tex] = Inner radius = 2.98 cm

l = Length of cylinder

[tex]\epsilon_0[/tex] = Permittivity of free space = [tex]8.85\times 10^{-12}\ F/m[/tex]

V = Volume

E = Electric field

Charge is given by

[tex]Q=\rho V\\\Rightarrow Q=\rho\pi l(r_o^2-r_i^2)[/tex]

Area

[tex]A=2\pi rl[/tex]

From Gauss law the flux through a cylindrical surface is given by

[tex]EA=\frac{Q}{\epsilon_0}\\\Rightarrow E=\frac{Q}{\epsilon_0A}\\\Rightarrow E=\frac{\rho\pi l(r_o^2-r_i^2)}{\epsilon_02\pi rl}\\\Rightarrow E=\frac{\rho(r_o^2-r_i^2)}{\epsilon_02r}\\\Rightarrow E=\frac{9.22\times 10^{-3}(0.035^2-0.0298^2)}{8.85\times 10^{-12}\times 2\times 0.0735}\\\Rightarrow E=2388078.86544\ N/C[/tex]

The electric at the given distance is 2388078.86544 N/C

Answer:

Protons

Explanation:

All the atoms in the carbon sample will contain the same atomic number, represented by Z.

Also, the nucleus of an atom consists of protons and neutron and for the atomic number to be same, the number of protons in the atom must be same.

Therefore, the nucleus can have variation in the number of neutron but not proton for the same carbon sample giving rise to the isotopes of carbon.

Isotopes:

The elements that contains the same atomic number but their mass number is different.

Answer:

0.577

Explanation:

The initial weight is

mg= [tex]\frac{GMm}{r_1^2}[/tex].......................1

and the final weight is

[tex]3mg= \frac{GMm}{r_2^2}[/tex]......................2

now to calculate [tex]r_2/r_1[/tex]

now dividing equation 1 by equation 2 we get

[tex]\frac{1}{r_1^2}/\frac{1}{r_2^2}[/tex]= 1/3

[tex]\frac{r_2}{r_1} =\sqrt{\frac{1}{3} }[/tex]

[tex]\frac{r_2}{r_1}[/tex]=0.577

To calculate the value of 'do' in the given pulley system, we need to know the efficiency.

In order to calculate the value of 'do' in the given pulley system, we need to understand the concepts of actual mechanical advantage (AMA) and ideal mechanical advantage (IMA).

AMA is the ratio of the output force (load) to the input force (effort). In this case, the load is the engine with a weight of 2,000 newtons and the effort force is 250 newtons. So, AMA = Load/Effort = 2000 N/250 N = 8.

IMA is the theoretical mechanical advantage calculated by counting the number of ropes supporting the load. In this case, since there is only one rope supporting the load, IMA = 1.

The relationship between AMA and IMA is given by the equation: AMA = IMA x efficiency.

Since the efficiency is not provided in the question, we cannot directly calculate the value of 'do' without this information.

Answer: 3.5units

Explanation:

Gravitational force existing between the two masses is directly proportional to the product of their masses and inversely proportional to the square of the distances between the masses.

Mathematically, F = GMm/r^2

G is the gravitational constant

M and m are the masses

r is the distance between the masses.

If the force of attraction between the masses is 16units, it becomes,

16 = GMm/r^2... (1)

If the mass of object 1 is doubled and distance tripled, we will have

F= G(2M)m/(3r)^2

F=2GMm/9r^2... (2)

Solving eqn 1 and 2 to get the new Force

Dividing eqn 1 by 2, we have

16/F = GMm/r^2 ÷ 2GMm/9r^2

16/F = GMm×9r^2/r^2×2GMm

16/F = 9/2(upon cancelation)

Cross multiplying we have

9F=32

F= 32/9

F= 3.5units

Answer:

Answer: F = 4 units

Explanation:

If the distance is increased by a factor of 2, then force will be decreased by a factor of 4 (22). The new force is then 1/4 of the original 16 units.

F = (16 units ) / 4 = 4 units

Answer:

Straight Line

Explanation:

For an ideal gas,

PV = nRT

For a fixed quantity ( constant number of moles) of a gas at fixed temperature

Right side of the equation will be constant

Thus,

PV = C

So, P = [tex]\frac{C}{V}[/tex] .

Thus P is directly related to [tex]\frac{1}{V}[/tex]

That's why plot between P and  [tex]\frac{1}{V}[/tex] will be an straight line.