Our solar system is in the Milky Way galaxy. In another galaxy a planet, P, has a circular orbit equal to that of the Earth's, that is, the orbits have the same radius. The masses of the suns in the two galaxies are Sg and Sp respectively and planet P completes its orbit in half the time it takes the Earth. (i) Show that the mass of the Sun in the Earth's orbit is four times the mass of the sun in Planet P's orbit.
(ii)Show that the period of the planet, P, is given by T = 2₁√ √/GM₂ where Mp is the mass of the planet and r the radius of the orbit​

volume of the pool= area of trapezium × breadth , the mass of water in the pool is = 144000.

One H2O molecule weighs 18.02 amu on average.The number of atoms and molecules is an exact number; neither of these factors affects the amount of significant figures.An average mole of water weighs 18.02 grams.It is reported that water has a molar mass of 18.02 g/mol.

Answer and justification One gram of water makes up one milliliter.Since water has a density of 1 g/ml, 1 ml of volume of water corresponds to 1 g of mass.

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Answer:

Explanation:

Momentum (p) = mass(m) x velocity(v)

v = 12m/sec , m= 20kg

p=20*12 = 240 kg m s−1 or 240 Ns

As the volume rises, the equilibrium shifts to the left, favoring the reactants. As the volume is decreased, the equilibrium will shift toward the component of the reaction in which there are fewer moles.

An object is considered to be operating in unstable equilibrium when ever a destructive force is applied if the center of mass is lowered and the object moves from its starting position.

Equilibrium is important for understanding chemical processes since it tells us how the reaction will proceed. We can control the reaction's parameters to help the creation of desirable products while it is in equilibrium. It is also used to calculate the final reaction mixture's composition.

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Each ball has an electric field surrounding it, and the magnet creates a magnetic field as well.

The area of space surrounding an electrical charges particle or object within which the charged body perceives force is known as the electric field .Examples: -Electric fields are created by charges and their configurations, such as capacitor and battery cells.

Each location in space at which a charge exists in any form can be regarded to have an electric field attached to it. The electrostatic force per mass unit is another name for an electric field. The electric field's equation is stated as E = F / Q.

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Answer:

D

Explanation:

I believe it is D, which is the resultant of the vector addition of B and E

At the origin, the electric field has a magnitude of [tex]\frac{k\lambda_0}{x_0}[/tex] and is oriented in a positive x-direction.

Coulomb's law may be used to determine the size of the electric field at the origin caused by a continuous line of charge:

[tex]E = \frac{kq}{r^2}[/tex]

Using the superposition principle, the electric field owing to a differential element of charge dq is:

[tex]dE = \frac{k dq} {r^2}[/tex]

Because the differential charge element is proportional to the linear charge density and the differential length, [tex]dq = \lambda_0 dx[/tex]. Because the distance r from the origin to the differential element equals [tex]r = x_0 + x[/tex],

[tex]dE = \frac{k\lambda_0 dx}{(x_0 + x)^2}[/tex]

Integrating this formula from x = 0 to x = infinity yields the total electric field at the origin:

[tex]E = k\lambda_0 \int_{0}^{\infty} \frac{dx}{(x_0 + x)^2}[/tex] from 0 to infinity

Using partial fractions, the integral may be calculated as follows:

[tex]E = \frac{k\lambda_0}{x_0}[/tex]

The linear charge density and the distance x0 from the closest point on the line of charge are both inversely correlated with the electric field at the origin.

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The ball will be moving at a velocity of 14.0 meters per second when it reaches the bottom of the ramp.

The velocity of the ball at the bottom of the ramp can be determined using the principle of conservation of energy. The potential energy of the ball at the top of the ramp will be converted into kinetic energy as it rolls down the ramp.

Potential energy = mgh

Kinetic energy = (1/2)mv²

At the bottom of the ramp, all of the potential energy has been converted into kinetic energy, so the equation can be written as:

mgh = (1/2)mv²

Solving for v, we have:

v = √(2gh)

where g is the acceleration due to gravity (9.8 m/s²). So, given the height h, we can calculate the velocity of the ball at the bottom of the ramp.

Let's assume the height of the ramp is h = 10 meters. Then, the velocity of the ball at the bottom of the ramp can be calculated as:

v = √(2gh) = √(2 × 9.8 m/s² × 10 m) = √(196 m²/s²) = 14.0 m/s

So, the ball will be moving at 14.0 meters per second when it reaches the bottom of the ramp.

It's important to note that the ball is rolling without slipping, meaning that its velocity is due to both its rotational motion and its translation. The velocity of the center of mass of the ball at the bottom of the ramp will be equal to the calculated velocity.

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(a) The number of waves on the diagram is 2.

(b) The period of the of the oscillation of the wave is 0.4 second.

(c) The frequency of the wave is 2.5 Hz.

The number of waves on the diagram is determined by calculating the number of cycles.

number of waves = 2

The period of the of the oscillation of the wave or the time taken to make a complete cycle is calculated as;

T = 0.4 seconds

The frequency of the wave is the reciprocal of the period of the wave and it is calculated as follows;

f = 1/T

f = 1 / 0.4

f = 2.5 H

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The ball was thrown a total distance of 52.7 meters. The maximum height of the ball is 8.8 meters.

The distance refers to the amount of space between two points. It is typically measured in units of length such as meters, kilometers, or miles. Distance can also be measured in terms of time, as in the distance between two points in terms of the amount of time it takes to travel between them. Distance is an important concept in mathematics and can be used to calculate the length of a line, the area of a shape, or the volume of an object.

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We fear too little for all those events that will claim lives undramatically.

Fear is an extremely unpleasant feeling that occurs when one perceives or recognizes a threat or danger. Fear results in physiological alterations that might result in behavioral responses like mounting an aggressive defence or running away from the threat.

Our physical, emotional, or let us consider psychological health may be at risk. While most of us have particular things that make us fearful, we can learn to be scared of almost anything that are around us.

Cortisol and adrenaline, two stress hormones, are released. Your heart rate and blood pressure rise. Your respiration quickens. Even your blood supply alters; blood actually moves out from your heart and towards your limbs, facilitating the initiation of punches or other physical attacks.

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It is not speeding up. It will therefore move 6 meters per second. The speed would have increased by 6 m/s per second if the item had been accelerating and the speed had been in the plane of the speed.

an object is moving at a constant speed, can it accelerate Yup Many individuals initially find this counter-intuitive because they overlook the fact that acceleration can still occur even when an object maintains a constant speed.

A motion of an object that does not alter over time is referred to as a constant acceleration. A car's average speed increases if it goes from 20 mph to another 20 mph in a minute.

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They have a limited supply in nature, therefore if they are used excessively, they will become exhausted.

Today, we recognise that using fossil fuels has a negative impact on the environment. Fossil fuels produce and utilise local pollutants, and their continued use permanently alters the temperature of our entire world.

Wastes from combustion sources are those that result from carbon pollution (i.e., coal, oil, natural gas). Included in this are all ash and particles taken out of the flue gas.

The fossile fuel is limited in nature. So, it should not waste energy from fossil fuels.

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The radius of the turn for the falcon flying at 22 m/s is approximately equal to: radius ≈ 5.18 m.

The centripetal acceleration required for a tight circular turn can be calculated using the formula:

centripetal acceleration = velocity² / radius

where velocity is the speed of the falcon and radius is the radius of the turn.

Given that the centripetal acceleration is 1.5 times the free-fall acceleration (g), we can write:

centripetal acceleration = 1.5 × g = 1.5 × 9.8 m/s²

Substituting this value into the above equation and solving for the radius, we get:

radius = velocity² / centripetal acceleration = (22 m/s)² / (1.5 × 9.8 m/s²) = (22²) / (1.5 × 9.8) m.

So the radius of the turn for the falcon flying at 22 m/s is approximately equal to: radius ≈ 5.18 m.

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Therefore the speed at the ground is 185. 3 m/s.

horizontal speed = 485 km/hr

= 485 * (5/18)

= 134.72m/s

h = 875 m

g = 9.8 m/s^2

a) Using formula,

h = (1/2) gt^2

875 = (9.8/2) t^2

t = 13.36 seconds

b)

D = u * t

D = 131.11 * 13.36

D = 1751.64 m

D = 1.75 km

c) when it lands on the ground

Vx = 131.11 m/s

Vy = gt

= 9.8 * 13.36

= 130.9 m/s

Therefore the speed at ground = [ 131.11^2 + 130.9^2]^(1/2)

= 185. 3 m/s

The pace is the directional speed of an item in motion as a demonstration of its price of alternate in the role as observed from a specific body of reference and as measured via a particular widespread of time (e.g. 60 km/h northbound). speed is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of our bodies.

Velocity is a bodily vector amount; each significance and route are needed to define it. The scalar absolute value (significance) of speed is known as velocity, being a coherent derived unit whose quantity is measured inside the SI (metric device) as meters in step with second (m/s or m⋅s−1). as an example, "5 meters in step with 2d" is a scalar, whereas "5 meters consistent with 2nd east" is a vector. If there is a trade-in velocity, route, or each, then the object is stated to be present process an acceleration.

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Momentum is conserved in this collision.

Momentum is conserved in this collision. To show this, we can calculate the initial momentum of the system and compare it to the final momentum.

Initial momentum:

12.5 kg * 4 m/s + 10 kg * -2 m/s = 50 kg m/s

Final momentum:

12.5 kg * -1.6 m/s + 10 kg * 5 m/s = 50 kg m/s

As we can see, the initial momentum is equal to the final momentum, so momentum is conserved in this collision.

This is because momentum is a conserved quantity, which means that it can be neither created nor destroyed, only transferred from one body to another. In this case, the momentum of the 12.5 kg ball was transferred to the 10 kg ball, and the final result was that the momentum of the system remained unchanged.

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In  an open system, Matter, heat and work are able to freely enter or exit the system. Hence, option (A) is correct.

A system that interacts with the outside world is an open system. Depending on the field that defines the term, these interactions can involve the transfer of information, energy, or materials into or out of the system border.

An isolated system, which does not exchange energy, matter, or information with its surroundings, is contrasted with an open system. A flow system is another name for an open system. Hence, option (A) is correct.

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The instantaneous velocity of an object can differ from its average velocity if the object is accelerating, that is, if its velocity is changing with time.

What is instantaneous velocity?

Instantaneous velocity is the speed of an object at a specific moment in time. It is the limit of the average velocity over an infinitesimal time interval as the interval approaches zero. In other words, it is the rate of change of an object's position with respect to time at a specific moment.

Average velocity is calculated as the total displacement divided by the time interval, but it does not take into account changes in velocity that occur during that time interval. In contrast, instantaneous velocity is the velocity of an object at a particular moment in time, and it can be different from the average velocity if the object's velocity changes over time.

Therefore, The instantaneous velocity of an object can differ from its average velocity if the object is accelerating, that is, if its velocity is changing with time.

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Revolving doors have three or four leaves (or wings) that are centered on a vertically oriented central pivoting shaft. These are contained in a spherical enclosure having openings on the interior and outside to permit movement when the door rotates within the enclosure.

Revolving doors can be run either manually or mechanically.If something is a "revolving door," it means that people or other items are constantly coming and going rather than remaining in one place: Ten directors came and departed over a twelve-year period, making the department a revolving door for senior executives.

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According to the solving using gravitational law the earths  its orbital period = 5.6 hours.

Every particle in the universe is drawn to every other component with a force that is directly related to the product between their masses and inversely proportional to their separation from one another, according to Newton's Law of Universal Gravitation. As a result, the general gravitation equation takes shape. F ∝ m 1 m 2 r 2.

Newton's first law asserts that an object at rest will stay at rest and also an object in motion will keep moving at a fixed pace unless they are both subject to a net external force.

The strength of attraction between two particles can be expressed as follows, according to Newton's gravitational law:

F = [tex]G\frac{M_1M_2}{R^2}[/tex]

speed of satellite = v = 5000 m/s

mass of earth = M = 6 × 10²⁴ kg

orbital period = T = ?

∑F = ma

[tex]G\frac{mm_2}{R^2}[/tex] = M[tex]\frac{v^2}{r}[/tex]

Substituting the value we get:

T = 2πG[tex]\frac{M}{v^3}[/tex]

T = 2π ×  6.67 × 10⁻¹¹ [tex]\frac{ 6 * 10^2^4}{5000^3}[/tex]

T = 20116s

T = 5.6 hours.

According to the solving the earths  its orbital period = 5.6 hours.

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The separation between the double slits is  0.0506 mm.

Interference in physics is a phenomena when two waves merge by adding their displacements at each and every point in space and time to produce a new wave that has a higher, lower, or identical amplitude.

The angular separation is = 6.5° = 6.5 × π/180

Wavelength of light is = 575 nm =  575 × 10⁻⁹ m

Let the separation between the double slits = d m.

Then;

6.5 × π/180 = 575 × 10⁻⁹/d

d = 5.06 × 10⁻⁶ meter

= 0.0506 mm.

Hence, the separation between the double slits is  0.0506 mm.

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The buoyant force acting on the object submerged in mercury is 133,176 V N/m^3.

What is Buoyant force?

The buoyant force is caused by the pressure difference that exists between the top and the bottom of an object immersed in a fluid. The pressure at the bottom of the object is greater than the pressure at the top, due to the weight of the fluid above it. This difference in pressure creates an upward force, which is called the The buoyant force acting on the object submerged in mercury is 133,176 V N/m^3.

Buoyant force = weight of displaced fluid

The weight of the displaced fluid is equal to the density of the fluid times the volume of the displaced fluid times the acceleration due to gravity (9.81 m/s^2).

Let's assume that the object has a volume of V and a weight of W.

Since the object is submerged in mercury, the weight of the displaced mercury is equal to the weight of the object (W), so we can write:

Weight of displaced fluid = W

Density of mercury = 13,600 kg/m^3

Volume of displaced fluid = V

Acceleration due to gravity = 9.81 m/s^2

Therefore, the buoyant force acting on the object is:

Buoyant force = Weight of displaced fluid

= Density of fluid x Volume of displaced fluid x Acceleration due to gravity

= 13,600 kg/m^3 x V x 9.81 m/s^2

= 133,176 V N/m^3

So, the buoyant force acting on the object submerged in mercury is 133,176 V N/m^3.

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The potential energy stored in the spring when it is displaced a distance "x" from the equilibrium position is [tex]U = (k/4)x^4.[/tex]

The potential energy stored in a spring can be calculated using the work-energy theorem, which states that the work done on an object is equal to the change in its potential energy. If the spring is displaced a distance "x" from the equilibrium position, the force exerted by the spring is given by the equation[tex]f = kx^3[/tex], where "k" is a constant of proportionality. The work done on the spring as it is displaced a distance "x" is given by the equation [tex]W = ∫f dx = ∫kx^3 dx.[/tex]

To find the potential energy stored in the spring, we can evaluate the definite integral:

U =[tex]∫kx^3 dx = (k/4)x^4 + C,[/tex]

where "C" is a constant of integration. The constant "C" can be determined by specifying the potential energy to be zero when the spring is at its equilibrium position, so that U = 0 when x = 0. This gives us:

[tex]C = -(k/4) * 0^4 = 0[/tex],

So the potential energy stored in the spring when it is displaced a distance "x" from the equilibrium position is:

[tex]U = (k/4)x^4.[/tex]

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The radiation radiated from an area A on a black body at actual temperature T is directly in proportion to the fourth power of a temperature, according to Stefan Boltzmann's law.

What significance do ratio and proportion have?

The ratio and ratio are important building blocks for understanding the numerous ideas in science and mathematics. Several challenges in daily life can be solved with proportion, including those in business when handling transactions or in the kitchen, among other situations. It creates a relationship among two or more numbers and aids in comparing them.

What would a proportional statement look like in practice?

For instance, the proportion statement for the ratio 45 is 20/25 = 45. This proportional statement can be solved to yield: The relationship between two quantities, such as a:b, when b is not equal to 0, is thus defined by the ratio. Example: 2:4 = 1:2 is used to show the proportion of 2 to 4. Here, it is claimed that the statement is in proportion.

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Fermat's Theorem states that the path taken by a wave traveling from one point to another in a medium is the path that takes the least time, which is applicable in fluid dynamics to explain why fluids tend to follow the path of least resistance.

Fermat's theorem, also known as the "principle of least time," states that the path taken by a wave traveling from one point to another in a medium is the path that takes the least time.

In fluid dynamics, this principle is used to explain why fluids tend to follow the path of least resistance, as they seek to minimize the time it takes to move from one point to another. This results in the fluid flowing along the path of least energy, which is also known as the path of least resistance. The principle of least time is used to predict the behavior of fluids under different conditions, and it is an important concept in the field of fluid dynamics.

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The required force between the two charges, when the distance between them is specified is calculated to be 416.67 N.

The charge q₁ is given as 0. 00005 C.

The charge q₂ is given as 0. 00003 C.

The separation (r) between the two charges is given as, 1.8 m.

The expression to find out the force between two charges is given as,

F = k q₁ q₂/r²

where,

k is relative permittivity (9 × 10⁹N)

q₁, q₂ are charges

r is separation between charges

Substituting the known values,

F = k q₁ q₂/r² = (9 × 10⁹× 5 × 10⁻⁴ × 3 × 10⁻⁴)/1.8² = 1350/1.8² = 416.67 N

Thus, the required force is calculated to be 416.67 N.

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1. The spring force constant that attach a block with a mass of 0.3 kg = 15 N/m

2. The amplitude of the motion = 1.85 m

3. The maximum speed of the block during its motion = 6.9 m/s

4. The maximum magnitude acceleration of the block's acceleration during its motion = 92.5 m/s²

The force a spring applies to objects fastened to its ends is proportional to the distance the spring travels from its equilibrium length and is always pointed in the direction of equilibrium. F = -kx. The term "spring constant" refers to the proportional constant k.

The block's weight and the spring's force are equal:

F = -kx

ma = -kx

Hence,

1.

The spring force constant (k) = - (ma) / x

= - (0.3 x (-12) / 0.24

= 15 N/m

The total energy system:

E = [tex]\frac{1}{2}[/tex] (mv² + kx²)

= [tex]\frac{1}{2}[/tex] {(0.3 x 4)² + (15 x 0.24)²}

= 7.2 J

2.

The amplitude of the motion =

E = [tex]\frac{1}{2}[/tex] (mv² + kA²)

A = [tex]\sqrt{E^{2}/k }[/tex]

= [tex]\sqrt{\frac{(7.2)^{2} }{15} }[/tex]

= 1.85 m

3. The maximum speed of the block during its motion

E =  [tex]\frac{1}{2}[/tex] mv² + 0

v = [tex]\sqrt{\frac{2E}{m} }[/tex]

= [tex]\sqrt{\frac{2(7.2)}{0.3} }[/tex]

= 6.9 m/s

4. The maximum magnitude acceleration of the block's acceleration during its motion =

ma = kA

a = kA/m

= (15 x 1.85) / 0.3

= 92.5 m/s²

The question is incomplete, it should be:

A block with a mass of 0.3 kg is attached to one end of an ideal spring the other end is attached to a wall. when the block is at 0.24m, its acceleration is -12 m/s2 and its velocity is 4 m/s. find:

1. What is the spring's force constant k?2. What is the amplitude of the motion?3. What is the maximum speed of the block during its motion?4. What is the maximum magnitude of the block's acceleration during its motion?

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The water that had been contracting as it cooled would start to expand. Option C

We have to note that the liquid that we have inside the thermometer is what we call the thermometric liquid. This is the kind of liquid that would increase in volume or decrease in volume so that the temperature can be measured.

We must note that water has an anomalous behavior and this is one of the reasons that stops water from being used as a thermometric liquid. This is the fact that water would begin to expand at about 4 degrees centigrade.

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The required maximum mass that the beam can bear without slipping is 14.163 kg.

The maximum mass that a 4.0 m long steel beam with a cross-sectional area of 1.0 × 10²m² and a Young's modulus of 2.0 × 10' N/m² can bear without slipping when wedged horizontally between two vertical walls and compressed by 0.020 mm, assuming a coefficient of static friction of 0.70, is calculated as follows,

Force of friction = coefficient of static friction × normal force = Area of beam × Young's modulus × compression

Therefore, the force of friction = 0.70 × (1.0 × 10² m²) × (2.0 x10' N/m²) × 0.020 mm

Maximum mass = (force of friction) / (acceleration due to gravity)

Therefore, the maximum mass that the beam can bear without slipping is (0.70 × (1.0 × 10² m²) × (2.0 × 10' N/m²) × 0.020 mm) / (9.81 m/s²) = 14.163 kg.

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Answer:

D) πR/7,200 m/s

Explanation:

Let's call the speed of the moon "v".

We know that the period (T) of the moon is given by: T = 20 hours = 20 hours * 3600 seconds/hour = 72000 seconds

We can relate the speed of the moon to its period and distance using the formula:

v = 2πR/T, where R is the distance of the moon from the center of the planet.

In this case, the distance is 5R, so:

v = 2π(5R)/T

= 2π(5R)/72000 seconds

= (πR)/7,200 seconds

So the speed of the moon is (πR)/7,200 m/s.

Therefore, the answer is D) πR/7,200 m/s.

Answer:

Explanation:

We know that distance can be calculated using the formula:

d = v0 * t + 0.5 * g * t^2

where v0= intial velocity

t=fall time

g= free fall acceleration

Now as per the question:

initial velocity v0 = 2.30 m/s

time t = 1.50 s

Free fall acceleration g = 9.8 m/s^2

d= v0 * t + 0.5 * g * t^2

distance = 2.30 * 1.50 + 0.5 * 9.8 * 1.50^2

distance = 3.45 + 14.7

d = 18.15 m

Therefore, the swimmer lands 18.15 meters from the base of the starting block.