See attachment for the question

a) The capacitance of the ceramic capacitor is approximately 354.16 pF.

b) The potential difference between the plates of the capacitor will be approximately 3.39 x 10^6 volts.

To calculate the capacitance of the ceramic capacitor, we can use the formula:

C = (ε₀ * εᵣ * A) / d

where:

C is the capacitance,

ε₀ is the vacuum permittivity (approximately 8.854 x 10^(-12) F/m),

εᵣ is the relative permittivity of the ceramic (given as 100),

A is the effective plate area (given as 4 cm², which is equal to 4 x 10^(-4) m²),

d is the separation between the plates (given as 0.1 mm, which is equal to 0.1 x 10^(-3) m).

Let's calculate the capacitance in picofarads (pF):

a) Calculation of capacitance (C):

C = (ε₀ * εᵣ * A) / d

= (8.854 x 10^(-12) F/m * 100 * 4 x 10^(-4) m²) / (0.1 x 10^(-3) m)

= (8.854 x 100 x 4) / 0.1

= 354.16 pF

Therefore, the capacitance of the ceramic capacitor is approximately 354.16 pF.

b) To find the potential difference (PD) between the plates when the capacitor is given a charge of 1.2 μC (microcoulombs), we can use the formula:

PD = Q / C

where:

PD is the potential difference,

Q is the charge (given as 1.2 μC, which is equal to 1.2 x 10^(-6) C),

C is the capacitance (calculated in part a) as 354.16 pF, which is equal to 354.16 x 10^(-12) F).

Let's calculate the potential difference (PD):

b) Calculation of potential difference (PD):

PD = Q / C

= (1.2 x 10^(-6) C) / (354.16 x 10^(-12) F)

= 3.39 x 10^6 V

Therefore, the potential difference between the plates of the capacitor will be approximately 3.39 x 10^6 volts.

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Answer:

(a) The hydrostatic pressure at the bottom of the tank is 12,054 Pa

(b) The hydrostatic force at the bottom of the tank is 289,296 N

(c) The hydrostatic force on one end of the tank is 36,162 N

Explanation:

The dimensions of the tank are;

The length of the tank, l = 6 m

The width of the tank, w = 4 m

The height of the tank, h = 2 m

The density of kerosene in the tank, ρ = 820 kg/m³

The depth of kerosene in the tank, d = 1.5 m

The acceleration due to gravity, g = 9.8 m/s²

(a) The hydrostatic pressure at the bottom of the tank, 'P', is given by the following formula

P = ρ·g·h

P = 820 kg/m³ × 9.8 m/s² × 1.5 m = 12,054 Pa

The hydrostatic pressure at the bottom of the tank, P = 12,054 Pa

(b) The hydrostatic force at the bottom of the tank, F = P × A

Where;

A = The area of the base of the tank = l × w

∴ A = 6 m × 4 m = 24 m²

∴ F = 12,054 Pa × 24 m² = 289,296 N

The hydrostatic force at the bottom of the tank, F = 289,296 N

(c) Taking one end of the tank as one of the width (4 m) side of the tank, the hydrostatic force on one end of the tank, \(F_E\), is given as follows;

The cross-sectional area of a layer, \(A_i\) = 4·dy

Therefore, the pressure at a given depth, \(P_i\) = ρ·g·\(y_i\)

The force at the given depth, \(F_i\) = \(A_i\) × \(P_i\)

∴ \(F_i\) = \(P_i\)·4·dy = ρ·g·\(y_i\)·4·dy

The force at the given depth, \(F_i\) = ρ·g·\(y_i\)·4·dy

The force at one end, \(F_E\)

\(F_E\) = \(\int\limits^{1.5}_0 {F_i \, dy = \int\limits^{1.5}_0 {(4 \cdot \rho} \cdot g \cdot y) \, dy = \left [4 \cdot \rho} \cdot g \cdot \dfrac{y^2}{2} \right]^{1.5}_0 = 4 \times \rho} \times g \times\dfrac{1.5^2}{2}\)

∴ \(F_E\) = 4 m × 820 kg/m³ × 9.8 m/s² × (1.5²)/2 m² = 36,162 N

The hydrostatic force on one end of the tank, \(F_E\) = 36,162 N

(For the length side, the force is 6×820×9.8×(1.5²)/2 = 54,243 N)

Given that the initial speed of the plane is u = 120 m/s

The final velocity of the plane is v = 0 m/s as the plane comes to rest.

The plane has an acceleration, a = -5.30 m/s^2.

We have to find the minimum time required for the plane to stop.

The required kinematic equation is

Substituting the values, the time will be

Thus, the minimum time required to stop the plane is 22.64 s.

Advantages:

From Charles's law, the magnitude of the final temperature is 586 K

An Ideal gas is a gas which obeys ideal gas equation at all pressures, volumes and temperatures. The ideal gas equation can be express as

PV = nRT

Where

Given that 1000 cm³ of air at 20 °C and 101.35 kPa is heated at constant pressure until its volume doubles.

From the ideal gas equation,

To calculate the final temperature of the gas, we will use the formula below

V1/T1 = V2/T2

Since Pressure is constant

Substitute the necessary parameters into the formula

1000/293 = 2000/T2

Cross multiply

1000T2 = 586,000

T2 = 586,000/1000

T2 = 586 K

Therefore, the final temperature of the gas is 586 K

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Answer: The diagram of the circuit is missing but I will give you a general answer based on the scope of your question

Answer : Parallel circuit

Explanation:

When a light bulb goes off and the other lightbulbs continues to glow, then the circuit connecting the lightbulbs is a Parallel circuit.

Hence the circuit that is built so that one lightbulb can go out and the other three lightbulbs will continue to glow as seen in the question fits the description above.

A parallel circuit allows the continuous flow of current even when some path of the circuit is cut off .

Answer:

Parallel circuit

Explanation:

Parallel series or circuits have the inherent advantage that perhaps the exhaustion or elimination of one bulb does not affect the other lights in the circuit. Since there is still a different, isolated closed path first from output to one of the other modules, they continue to function. So, we use Parallel series or circuits.

Answer:

1.47 m/s

Explanation:

v = v0 + at

where

v0 = initial velocity (zero in this case)

a = acceleration = 0.21 m/s^2

t = time = 7 seconds

Plugging in these values, we get:

v = 0 + (0.21 m/s^2)(7 s)

v = 1.47 m/s

Answer:

Option A. 4 m

Explanation:

Please see attached photo for diagram.

In the attached photo, X is the distance from the centre to which the student on the right must sit in order to balance the seesaw.

Clockwise moment = X × 45

Anticlock wise moment = 3 × 60

Clockwise moment = Anticlock wise moment

X × 45 = 3 × 60

X × 45 = 180

Divide both side by 45

X = 180 / 45

X = 4 m

Thus, the student must sit at 4 m from the centre.

The distance from the center the student on the right will be if they want the

seesaw to stay parallel to the ground is 4m

The question tells us that X is the distance to the center , each side of the

see saw is 5m with total length being 10m. This is explained in the

attached picture.

Clockwise moment = X × 45

Anticlock wise moment = 3 × 60

Clockwise moment = Anticlock wise moment

X × 45 = 3 × 60

X × 45 = 180

           = 180 / 45

            = 4m

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Answer: An jack makes changing a tire easier because it lifts up the car to get the tire off of the ground.

Explanation:

Answer:

4.16×103 m/s

Explanation:

12. The time taken for the journey is 400 s

13. The time taken for the train is 200 s

14. The time taken is 7 h

15. The time taken for the beetle is 12 s

16. The time taken for the journey is 0.0068 h

The time taken in each case as given by the question can be obtain as follow:

12. The time taken for the journey

Time taken = Distance / Speed

Time taken = 26000 / 65

Time taken = 400 s

13. The time taken for the train

Time taken = Distance / Speed

Time taken = 3200 / 16

Time taken = 200 s

14. The time taken to travel

Time taken = Distance / Speed

Time taken = 672 / 96

Time taken = 7 h

15. The time taken for the beetle

Time taken = Distance / Speed

Time taken = 1.08 / 0.09

Time taken = 12 s

16. The time taken for the journey

Time taken = Distance / Speed

Time taken = 35 / 5147

Time taken = 0.0068 h

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Two forces f1=(8i+3j)N and f2=(4i+6j) are acting on 5kg object then  the magnitude of the resultant force is 15 N and the direction of the resultant force is approximately 36.87 degrees from the positive x-axis.

The acceleration of the object in the x-component (\(a_x\)) is 2.4  \(m/s^{2}\), and the acceleration in the y-component (\(a_y\)) is 1.8  \(m/s^{2}\).

The magnitude of the acceleration of the object is 3  \(m/s^{2}\).

To find the magnitude and direction of the resultant force, we need to add the two given forces together.

Given:

f1 = (8i + 3j) N

f2 = (4i + 6j) N

To find the resultant force (\(F_res\)), we simply add the corresponding components:

\(F_res\) = f1 + f2

= (8i + 3j) + (4i + 6j)

= (8 + 4)i + (3 + 6)j

= 12i + 9j

The magnitude of the resultant force (\(|F_res|\)) can be found using the Pythagorean theorem:

\(|F_res|\)= \(\sqrt{(12^2) + (9^2)}\)

= \(\sqrt{144 + 81}\)

= \(\sqrt{225}\)

= 15 N

So, the magnitude of the resultant force is 15 N.

To find the direction of the resultant force, we can use trigonometry. The direction can be represented by the angle θ between the positive x-axis and the resultant force vector. We can calculate θ using the inverse tangent function:

θ = arctan(9/12)

= arctan(3/4)

≈ 36.87 degrees

Therefore, the direction of the resultant force is approximately 36.87 degrees from the positive x-axis.

Now let's calculate the acceleration of the object in the x and y components. We know that force (F) is related to acceleration (a) through Newton's second law:

F = ma

For the x-component:

\(F_x\)= 12 N

m = 5 kg

Using  \(F_x\)= \(ma_x\), we can solve for \(a_x\):

12 N = 5 kg * \(a_x\)

\(a_x\)= 12 N / 5 kg

\(a_x\) = 2.4 \(m/s^{2}\)

For the y-component:

\(F_y\) = 9 N

m = 5 kg

Using \(F_y\) = \(ma_y\), we can solve for \(a_y\):

9 N = 5 kg * \(a_y\)

\(a_y\) = 9 N / 5 kg

\(a_y\)= 1.8  \(m/s^{2}\)

So, the acceleration of the object in the x-component (\(a_x\)) is 2.4  \(m/s^{2}\), and the acceleration in the y-component (\(a_y\)) is 1.8  \(m/s^{2}\).

To find the magnitude of the acceleration (|a|), we can use the Pythagorean theorem:

|a| = \(\sqrt{(a_x^2) + (a_y^2)}\)

= \(\sqrt{(2.4^2) + (1.8^2}\)

= \(\sqrt{5.76 + 3.24}\)

= \(\sqrt{9}\)

= 3  \(m/s^{2}\)

Therefore, the magnitude of the acceleration of the object is 3  \(m/s^{2}\)

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A beaver runs at a speed of 2.0 m/s with 45 J of kinetic energy, then the mass is approximately 1.74 kg, and this can be calculated by using the  kinetic energy (KE) of an object that is KE = (1/2) ×m × \(v^2\).

KE = (1/2) ×m × \(v^2\).

where m= mass of the object, v=its velocity.

The beaver runs at a speed of 2.0 m/s with 45 J of kinetic energy. Substituting these values into the above equation

45 J = (1/2) ×m × \((2.0 m/s)^2\)

Simplifying this equation:

45 J = (1/2) × m × 4.0\(m^2/s^2\)

45 J = 2 m × 2 \(m^2/s^2\)

45 J = 4 \(m^3/s^2\)

\(m^3\) = 45 J / 4 \(s^2\)

\(m^3\) = 11.25 kg×\(m^2/s^2\)

Taking the cube root of both sides to solve for mass,

m = (11.25 kg×\(m^2/s^2)^(^1^/^3^)\)

m = 1.74 kg (rounded to two decimal places)

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Based on Hooke's law, the spring constant of the the body's muscle mechanism is the ratio of force to extension, the effective mass is m/3 and the potential energy that can be stored is ke^2 / 2.

The spring constant or stiffness constant of an elastic spring is constant which describes the extent a bit forceapplied to an elastic spring will extend it.

Assuming, a body's muscle mechanism is a spring obeying Hooke's law, the effective mass of the spring with mass m is 1/3 of the mass of the spring = m/3

The potential energy that can be stored = ke^2 / 2

where K is spring constant and e is the extension produced.

Therefore, the spring constant of the the body's muscle mechanism is the ratio of force to extension, the effective mass is m/3 and the potential energy that can be stored is ke^2 / 2.

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From the darkest part of the object's shadow, you would be able to see a small amount of the light source. There would be a small amount of light that is visible, but it would be faint. On the other hand, from the lightest part of the shadow, you would be able to see much more of the light source. The light source would be far brighter and more visible, and you would be able to identify the source of the light.

Imagine you have three flashlights. One has a blue light, one has a green light and one is red. If you were to shine each of those lights in the same spot, I think i would see white color.

At one end of the electromagnetic wave line, which has the group of the visible spectrum. This has been referred to as the visible light of the spectrum. The visible light with the shortest of the wavelength has the blue light and the one with the longest has the red light.

The primary colors of the light has been the spectrum are red, blue, and green. The combination of these colors will form other as well as the colors which has been referred to as the secondary colors. The combination of the beam of the red light and the beam of green light will form yellow color.

Therefore, Imagine you have three flashlights. One has a blue light, one has a green light and one is red. If you were to shine each of those lights in the same spot, I think i would see white color.

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The charge on each particles which are 1 m apart and feeling a repulsive force of 1 N is 1.05×10¯⁵ C

Let the charge on each particles be q

The charge on each particle can be obtained by using the Coulomb's law equation as shown below:

F = Kq₁q₂ / r²

F = Kq² / r²

1 = (9×10⁹ × q²) / 1²

1 = 9×10⁹ × q²

Divide both side by 9×10⁹

q² = 1 / 9×10⁹

Take the square root of both side

q =  √(1 / 9×10⁹)

q = 1.05×10¯⁵ C

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As the settling distance is less than the chamber depth (1.0 m), the grit chamber can be expected to be effective in removing the particles with the given diameter.Using the Stoke's Law, the settling velocity is calculated as:

Stoke's Law is a scientific principle that states that the terminal settling velocity of a small sphere in a viscous fluid is inversely proportional to the fluid's viscosity. It is named after Sir George Gabriel Stokes, who first derived this law in 1851. Stoke's Law is important in many different fields, such as particle sedimentation, particle separation, and fluid mechanics. The law is also used to predict the settling velocity of particles in a fluid, which is important for applications such as filtration.

V = (2 x 9.81 x (1.71 x 10-4)2 x (1.83 - 1)) / (18 x 10-6 x (1 - 0.01))

= 1.39 x 10-4 m/s

The settling distance is calculated as:

S = V x T

= 1.39 x 10-4 x 60

= 0.00834 m

As the settling distance is less than the chamber depth (1.0 m), the grit chamber can be expected to be effective in removing the particles with the given diameter.

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The energy of a proton is given by:

where h is Planck's constant and f is the frequency. In this case the frequency is given, plugging the values we have:

Therefore, the energy is:

Answer:

C: 5

Explanation:

MA = radius of wheel/ radius of axle

MA =2.5/0.5

MA = 5.0

Answer:

the answer is push example: she thrust her hand into her pocket

Answer:

The answer is in the attachment

Explanation:

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Answer:

C. backhand stroke

Explanation:

Your hand will be rotated counterclockwise about a fourth of the racquet handle during this stroke. The correct response is to backhand stroke. Option C is correct.

When playing tennis, a backhand is a stroke in which the player's torso is crossed and the ball is struck with the palm towards the opponent's chest and the back of the hand traveling toward them.

A backhand in tennis can be made with one or both hands.

With this stroke, your hand will be turned about a quarter circle counter-clockwise on the handle of your racquet. Backhand stroke is the right answer.

Hence. option C is correct.

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The difference between fluid pressure at location 2 and fluid pressure at location 1 is mathematically given as

dP = 114 kPa

Parameters are :

density of liquid,

speed of flow at location 1, = 9.15m/s

diameter of pipe at location 1, = 12.3cm

diameter of pipe at location 2, = 16.1 cm

height of pipe at location 1, = 9.29 m

We know that the Bernoulli's equation is mathematically given as

P + ρ*g*y + v² =pipe  constant

Where

A1*v1 = A2*v2

π*(0.105/2)²*9.91 = π*(0.167/2)²*v2

v2 = 3.9 m/s

Hence, we have that

P1 + ρ*g*y1 + v1² = P2 + ρ*g*y2 + v2²

dP = 1290*9.8*9.01 + 9.91² - 3.9²

dP = 114 kPa

In conclusion, difference between fluid pressure is dP = 114 kPa

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Answer:

50s .

Explanation:

\(\frak{\pink{Given}}\begin{cases}\textsf{ The power of microvave is 0.2kW .}\\\textsf{ Amount of energy is 10000 J .}\end{cases}\)

Here the power of the microwave is 0.2kW . And as we know that ,

So from the definition , we have ;

\(\sf\longrightarrow Power =\dfrac{Work}{time}\)

\(\sf\longrightarrow Power =\dfrac{Energy}{time}\)

\(\sf\longrightarrow 0.2kW = \dfrac{10^4 J }{t} \\\)

\(\sf\longrightarrow 0.2 * 1000 W = \dfrac{10^4 J }{t} \)

Cross multiply ,

\(\sf\longrightarrow t = \dfrac{ 10^4 }{ 0.2 * 10^3}s=\dfrac{10^4}{2*10^2} s \)

Simplify ,

\(\sf\longrightarrow \boxed{\bf t = 50s} \)

The centripetal acceleration of an object under circular motion at constant speed v in a trajectory with radius r is:

Replace v=27.6m/s and r=195m to find the centripetal acceleration of the car:

Therefore, the car experiences an acceleration of 3.91 m/s^2.

According to Chargaff's rule, the amounts of adenine (A), thymine (T), and guanine (G) in the DNA molecule are equal to each other. The amounts of cytosine (C) and guanine (G) are also equal.

Erwin Chargaff was a biochemist, author, Bucovinian Jew who immigrated to America during the Nazi era, and professor of biochemistry at Columbia University's medical school.

Chargaff found patterns among the four bases, or chemical building blocks, of DNA, which are directly related to DNA's function as the genetic material of living things.

He was born in Austria-Hungary. Heraclitean Fire: Sketches from a Life Before Nature, an autobiography he penned, received positive reviews.

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Answer:

19.9 N/m

Explanation:

From the question,

Applying Hook's law

F = Ke.................. Equation 1

Where F = Force on the spring, k = spring constant, e = extension

But the force on the spring is the weight of the mass

Therefore,

mg = ke.................. Equation 2

Where m = mass. g = acceleration due to gravity

make e the subject of the equation

e = mg/e................ Equation 3

Given: m = 455 g = 0.455 kg, e = 22.4 cm = 0.224 m,

Constant: g = 9.8 m/s²

Substitute these values into equation 3

e = (0.455×9.8)/0.224

e = 19.9 N/m

The spring constant of the given spring is 20 N/m.

The given parameters:

The spring constant is calculated by applying Hooke's law as follows;

\(F = kx\\\\mg = kx\\\\k = \frac{mg}{x} \\\\k = \frac{0.455 \times 9.8}{0.224} \\\\k = 20 \ N/m\)

Thus, the spring constant of the spring is 20 N/m.

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