Part of my other question!

Gravitational force between two masses m, and m, is represented as F = Gm₂ m₂ / r^2 where r = xi+yj + zkG, m, m₂ are nonzero constants and let's assume that I = 0

a) Calculation:For F = Gm₂ m₂ / r^2.

Using r = xi+yj + zk and let r^2 = x^2 + y^2 + z^2∴ F = Gm₂ m₂ / (x^2 + y^2 + z^2), Where G, m, m₂ are nonzero constants. Divergence of F = ∇ · F= 1/r^2(d/dx(r^2Fx) + d/dy(r^2Fy) + d/dz(r^2Fz))= 1/r^2(d/dx(r^2Gm₂ m₂ x/(x^2+y^2+z^2)^(3/2)) + d/dy(r^2Gm₂ m₂ y/(x^2+y^2+z^2)^(3/2)) + d/dz(r^2Gm₂ m₂ z/(x^2+y^2+z^2)^(3/2)))= 1/r^2(d/dx(r^2Gm₂ m₂ x/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2) + d/dy(r^2Gm₂ m₂ y/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2) + d/dz(r^2Gm₂ m₂ z/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2))= 1/r^2(Gm₂ m₂ [2x(x^2+y^2+z^2)-3x^2]/(x^2+y^2+z^2)^(5/2) + Gm₂ m₂ [2y(x^2+y^2+z^2)-3y^2]/(x^2+y^2+z^2)^(5/2) + Gm₂ m₂ [2z(x^2+y^2+z^2)-3z^2]/(x^2+y^2+z^2)^(5/2))= 1/r^2(Gm₂ m₂ [(2x^2+2y^2+2z^2-3x^2)/(x^2+y^2+z^2)^(3/2)] + [2x^2+2y^2+2z^2-3y^2]/(x^2+y^2+z^2)^(3/2)] + [2x^2+2y^2+2z^2-3z^2]/(x^2+y^2+z^2)^(3/2)])= 1/r^2(Gm₂ m₂ [x^2+y^2+z^2]/(x^2+y^2+z^2)^(3/2))= 0.

Curl of F = ∇ × F= i(d/dy(Fz) - d/dz(Fy)) - j(d/dx(Fz) - d/dz(Fx)) + k(d/dx(Fy) - d/dy(Fx))= i(d/dy(Gm₂ m₂ z/(x^2+y^2+z^2)) - d/dz(Gm₂ m₂ y/(x^2+y^2+z^2))) - j(d/dx(Gm₂ m₂ z/(x^2+y^2+z^2)) - d/dz(Gm₂ m₂ x/(x^2+y^2+z^2))) + k(d/dx(Gm₂ m₂ y/(x^2+y^2+z^2)) - d/dy(Gm₂ m₂ x/(x^2+y^2+z^2)))= i(Gm₂ m₂ [-2xz]/(x^2+y^2+z^2)^(5/2)) - j(Gm₂ m₂ [-2yz]/(x^2+y^2+z^2)^(5/2)) + k(Gm₂ m₂ [(x^2+y^2-2z^2)]/(x^2+y^2+z^2)^(5/2))

b) Calculation:The line integral of F along a curve C can be evaluated by the following formula∫C F.dr = ∫∫ ( ∇ x F) ds, Where r is the position vector of the curve, s is the scalar parameter representing the curve, and the integral is evaluated from the initial point to the final point.

Using the curl of F obtained in part a) and for the surface with ∂S as C∫C F.dr = ∫∫ ( ∇ x F) ds= ∫∫ curl(F) ds= ∫∫ (-2xz i -2yz j + (x^2+y^2-2z^2)k) ds...[1]

Let's consider the surface S as a plane perpendicular to the z-axis of the form ax+by+c=0 and the curve C as the intersection of the plane and the cylinder x^2 + y^2 = a^2.

Let's choose the unit normal to the surface S as k (along the z-axis).

The curl of F is a vector field perpendicular to the plane and along the direction of k.

Thus the integral can be written as∫C F.dr = ∫∫ ( ∇ x F) . k ds= ∫∫ (x^2+y^2-2z^2) ds...[2]

Now let's evaluate the integral over the given plane ax+by+c=0. We can write x = t, y = (c-at)/b and z = 0, where t is the scalar parameter along the line of intersection of the plane and the cylinder (x^2 + y^2 = a^2).

Since the curve C is on the cylinder of radius a, we have x^2+y^2 = a^2 ⇒ t^2+(c-at)^2/b^2 = a^2On solving for t, we have t = (bc±ab √(a^2-b^2-c^2))/[a^2+b^2].

Substituting t in x and y, we get the curve C in the x-y plane as a function of the scalar parameter s asx = (bc±ab √(a^2-b^2-c^2))/[a^2+b^2]y = (c-at)/b= (c-(bc±ab √(a^2-b^2-c^2))/[a^2+b^2])/b.

Now we can evaluate the integral over the curve C, which is along the intersection of the plane and the cylinder.

Integral over C (x^2+y^2-2z^2) ds= ∫t₁^t₂ [(t^2 + [(c-at)^2]/b^2 - 2(0)^2)^(1/2)] dt= ∫t₁^t₂ [(a^2-b^2-c^2)t^2+2bc(c-at)+b^2c^2-a^2b^2]^(1/2) dt.

Now we can choose the value of t₁ and t₂ such that the square root in the integrand is minimized (so that the integral is path-independent).

This can be done by choosing the value of t that gives the minimum value of (a^2-b^2-c^2)t^2+2bc(c-at)+b^2c^2-a^2b^2 over the range of t from t₁ to t₂.

On differentiation with respect to t and equating to 0, we get the value of t = bc/(a^2+b^2).

Substituting this value of t in the integrand, we get the minimum value of the square root in the integrand to be |c| √(a^2+b^2)/|b|.

Thus the integral over C is given by∫C F.dr = ∫∫ (-2xz i -2yz j + (x^2+y^2-2z^2)k) ds= ∫∫ (x^2+y^2-2z^2) ds= ∫t₁^t₂ |c| √(a^2+b^2)/|b| dt= |c| √(a^2+b^2)/|b| (t₂-t₁).

Now we can see that the integral is path-independent as it depends only on the end points t₁ and t₂ and not on the path taken to reach them.

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Option B

Note that the current generated by an AC generator is an alternating current.

An alternating current is one which continually changes its polarity. That is, it oscillates and changes its magnitude and direction

Based on the points stated above, we can describe the current generated by an AC generator as a current that oscillates direction and magnitude between 0 and maximum.

This means that an alternating current does not only change its direction, it changes its magnitude too.

Answer: hope it helps you...❤❤❤❤

Explanation: If your values have dimensions like time, length, temperature, etc, then if the dimensions are not the same then the values are not the same. So a “dimensionally wrong equation” is always false and cannot represent a correct physical relation.

No, not necessarily.

For instance, Newton’s 2nd law is  F=p˙ , or the sum of the applied forces on a body is equal to its time rate of change of its momentum. This is dimensionally correct, and a correct physical relation. It’s fine.

But take a look at this (incorrect) equation for the force of gravity:

F=−G(m+M)Mm√|r|3r  

It has all the nice properties you’d expect: It’s dimensionally correct (assuming the standard traditional value for  G ), it’s attractive, it’s symmetric in the masses, it’s inverse-square, etc. But it doesn’t correspond to a real, physical force.

It’s a counter-example to the claim that a dimensionally correct equation is necessarily a correct physical relation.

A simpler counter example is  1=2 . It is stating the equality of two dimensionless numbers. It is trivially dimensionally correct. But it is false.

The cross in parental genotypes of Rr and Rr will have ¾ round and ¼ wrinkled of its phenotypes. The correct option is A.

The set of qualities or characteristics that can be observed in an organism are known as its phenotype in genetics.

The word includes an organism's anatomy, developmental processes, physiological and biochemical characteristics, behaviour, and the outcomes of behaviour.

In the given scenario, the alleles that will be formed are RR, Rr, and rr. The ratio of this will be 3:1.

It means, there will be 3 round phenotype out of 4 and one will be wrinkled.

Thus, the correct option is A.

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The surface area of the frustum generated by revolving the line segment joining the points (0, 5) and (7, 7) about the x-axis can be determined using parametrization.

To find the surface area of the frustum, we can use the method of parametrization. The frustum is formed by rotating the line segment about the x-axis, and we can parametrize the curve generated by the rotation.

Let's consider a parameter t that ranges from 0 to 1. We can express the x-coordinate of the curve as x = t * 7 and the y-coordinate as y = 5 + t * 2. The parameter t represents the progression along the line segment, ranging from 0 at the point (0, 5) to 1 at the point (7, 7).

To calculate the surface area, we need to find the differential element of arc length ds. For a curve given by parametric equations x = f(t) and y = g(t), the differential element of arc length can be expressed as ds = \(\sqrt{x} ((dx/dt)^2 + (dy/dt)^2) * dt\).

Substituting the parametric equations into the formula, we have ds = \(\sqrt((7^2 + 2^2)) * dt = sqrt(53) * dt.\)

To find the surface area of the frustum, we integrate ds from t = 0 to t = 1: \(Area =\int\limits^0_1 \, dx \sqrt(53) * dt.\)

Integrating this expression yields the surface area of the frustum. Therefore, by using parametrization and evaluating the integral, the surface area of the frustum generated by revolving the line segment (0, 5) to (7, 7) about the x-axis can be determined.

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Answer:

Explanation:

A mechanical wave is a disturbance in matter that transfers energy through the matter. The matter through which a mechanical wave travels is called the medium (plural, media). ... They differ in how particles of the medium move when the energy of the wave passes through.

If a ball is given a push so that it has an initial velocity of 2 m/s down a certain inclined plane, then the distance it has rolled after t seconds is s = 2t + t². Then it takes 11 seconds for the velocity to reach 24 m/s. The correct option is D.

To find the time it takes for the velocity of the ball to reach 24 m/s, we need to solve for the time when the velocity function equals 24 m/s.

The velocity function is the derivative of the distance function, so we'll first find the derivative of the distance function s = 2t + t² with respect to time t:

ds/dt = d/dt(2t + t²)

ds/dt = 2 + 2t

Now we can set the velocity function equal to 24 m/s and solve for t:

2 + 2t = 24

Subtracting 2 from both sides:

2t = 22

Dividing both sides by 2:

t = 11

Therefore, it takes 11 seconds for the velocity to reach 24 m/s.

The correct answer is (d) 11 seconds.

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Answer:

a.the measurement or extent of something from end to end; the greater of two or the greatest of three dimensions of a body.

b.is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume.

c.Mass is a physical magnitude and general property of matter that expresses the inertia or resistance to change in motion of a body.

d.Mass is a physical magnitude and general property of matter that expresses the inertia or resistance to change in motion of a body.

e.

a)The total mechanical energy is 70.812 J. b) The total mechanical energy of the book at the instant it was released is 50.076 J. c) The height of the stadium is 2.9 meters.  

A. To calculate the total mechanical energy of the book, we need to consider its kinetic energy (KE), gravitational potential energy (PE), and elastic potential energy (PE_elastic). Since there is no information provided regarding elastic potential energy, we can assume it to be zero in this case.

The kinetic energy (KE) is given by the equation KE = 1/2 * m * v^2, where m is the mass and v is the velocity. In this case, the mass (m) of the book is 1.8 kg and the velocity (v) is 4.8 m/s. Plugging in these values, we have KE = 1/2 * 1.8 kg * (4.8 m/s)^2 = 20.736 J (joules).

The gravitational potential energy (PE) is given by the equation PE = m * g * h, where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height. The height (h) in this case is 2.9 meters. Plugging in these values, we have PE = 1.8 kg * 9.8 m/s^2 * 2.9 m = 50.076 J.

The total mechanical energy is the sum of the kinetic energy and gravitational potential energy: Total mechanical energy = KE + PE = 20.736 J + 50.076 J = 70.812 J.

B. When the book is released from the top of the stadium, its initial speed is zero since it is not moving yet. Therefore, the kinetic energy (KE) at that instant is zero. The gravitational potential energy (PE) can be calculated in the same way as before using the mass of the book (1.8 kg) and the height of the stadium.

Assuming the height of the stadium is given by h_stadium, we can use the equation PE = m * g * h_stadium. Since the book is at the top of the stadium, its height above the ground is equal to the height of the stadium, so h_stadium = 2.9 meters. Plugging in these values, we have PE = 1.8 kg * 9.8 m/s^2 * 2.9 m = 50.076 J.

The total mechanical energy at the instant the book was released is equal to the gravitational potential energy: Total mechanical energy = PE = 50.076 J.  

C. To determine the height of the stadium, we need to rearrange the equation for gravitational potential energy: PE = m * g * h. In this case, the mass (m) of the book is given as 1.8 kg, and the acceleration due to gravity (g) is approximately 9.8 m/s^2.  

Given that the total mechanical energy at the instant the book was released is equal to the gravitational potential energy, which is 50.076 J, we can substitute these values into the equation: 50.076 J = 1.8 kg * 9.8 m/s^2 * h_stadium.  

Rearranging the equation to solve for h_stadium, we have: h_stadium = 50.076 J / (1.8 kg * 9.8 m/s^2) = 2.9 meters.

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Answer:

It is positive

Explanation:

The area is only concentrated with red protons

The first rope's tension supports both masses:

T - (5.0 kg + 10.0 kg) g = 0   ===>   T = 147 N

The second rope's tension supports the second mass:

T - (10.0 kg) g = 0   ===>   T = 98 N

The tension in the first and second rope are; 147 Newton and 98 Newton respectively.

Given the data in the question

To find the Tension in each of the ropes, we make use of the equation from Newton's Second Laws of Motion:

\(F = m\ *\ a\)

Where F is the force, m is the mass of the object and a is the acceleration ( In this case the block is under gravity. Hence ''a" becomes acceleration due to gravity  \(g = 9.8m/s^2\) )

For the First Rope

Total mass hanging on it; \(m_T = m_1 + m_2 = 5.0kg + 10.0kg = 15.0kg\)

So Tension of the rope;

\(F = m\ * \ g\\\\F = 15.0kg \ * 9.8m/s^2\\\\F = 147 kg.m/s^2\\\\F = 147N\)

Therefore, the tension in the first rope is 147 Newton

For the Second Rope

Since only the block of mass 10kg is hang from the second, the tension in the second rope will be;

\(F = m\ * \ g\\\\F = 10.0kg \ * 9.8m/s^2\\\\F = 98 kg.m/s^2\\\\F = 98N\)

Therefore, the tension in the second rope is 98 Newton

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The fundamental on this string has a frequency of roughly 49.4 Hz.

The following formula can be used to determine a wave's speed on a string:

v = sqrt(T/μ)

where T is the string's tension and is the string's linear mass density (mass per unit length). By dividing the string's mass by its length, we may calculate :

μ = m/L = 2.1 g / 1.5 m = 1.4 g/m = 0.0014 kg/m

Substituting the values of T and μ into the formula for v, we get:

v = sqrt(95 N / 0.0014 kg/m) ≈ 148.3 m/s

The formula: can be used to determine the fundamental frequency on the string, or the lowest resonant frequency.

f = v / (2L)

where L is the length of the string. Substituting the values of v and L, we get:

f = 148.3 m/s / (2 × 1.5 m) ≈ 49.4 Hz

Therefore, The fundamental on this string has a frequency of roughly 49.4 Hz.

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Answer:

5 m/s²

Explanation:

Acceleration = change in speed/time taken

20-5=15

15/3= 5 m/s²

Answer:

It will be B

Explanation:

Answer:The answer is B

Answer:

Momentum = Mass × velocity

by multiplying mass and velocity of that object , we can find out it's Momentum

P = M × V

Answer:

a. 25 N. The box will move toward the greater force, however, I'm not too sure if that is enough to move a 100kg box.

Explanation:

First, let's define resultant force.

Resultant force is the total force of action enacted on a object or thing.

To get the resultant force of this problem, add 10 N to 15 N and you will get an answer of 25 N total.

The object will move toward the greater force because there is a larger difference between the force on the left.

Answer:

b

Explanation:

The Coriolis effect is a condition which causes a hurricane to rotate in a particular direction. Thus, the correct option is B.

Hurricanes are the enormous storms which come with a rotating wind speed of about 74 miles per hour. The rotating wind that swirls across the warm water of the tropics and also comes with a terrifying force.

The Coriolis force is an inertial or the fictitious force, which acts on the objects which are in motion within a frame of reference that rotates them with respect to an inertial frame. In a reference frame, with the clockwise rotation, the force acts to the left of the motion of the object. Whereas, in one with anticlockwise or counterclockwise rotation, the force acts to the right of the object. The deflection of an object due to this Coriolis force is called as the Coriolis effect.

Therefore, the correct option is B.

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Answer:

3. 1.8A

Explanation:

Given the following data;

Quantity of charge, Q = 650C

Time = 6 minutes to seconds = 6 * 60 = 360 seconds.

To find the current l;

Quantity of charge = current * time

Substituting into the equation, we have;

650 = current * 360

Current = 650/360

Current = 1.8 Amperes

The plane travels a distance of 325 miles if the airplane travels for 2.5 hours at an average speed of 130 miles per hour. Using the distance formula (d = rt), we can calculate the distance.

To find the distance traveled by the airplane, we can use the distance formula, which is represented as d = rt. In this formula, "d" represents the distance, "r" represents the rate or speed at which the object is traveling, and "t" represents the time taken for the travel.

Given that the airplane travels for 2.5 hours at an average rate of 130 miles per hour, we can substitute these values into the formula. The rate of the airplane is 130 miles per hour, and the time taken is 2.5 hours.

Using the formula, we can calculate the distance traveled as follows:

d = rt

d = 130 mph × 2.5 hours

Multiplying the rate (130 mph) by the time (2.5 hours) gives us:

d = 325 miles

Therefore, the airplane travels a distance of 325 miles during the 2.5 hours of travel at an average rate of 130 miles per hour.

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For Each Of The Following Scenarios Described Where A Molecule Or Ion Is Moving From One Side Of A Membrane To The Other, Option A is correct answer.

Scenario A: Oxygen moving across a plasma membrane Answer: A. Simple Diffusion Scenario B: Glucose moving across a plasma membrane Answer: C. Facilitated Diffusion By A Carrier/Transport Protein Scenario C: Sodium moving across a plasma membrane Answer: B. Facilitated Diffusion By A Channel Protein Scenario D: Water moving across a plasma membrane Answer: A. Simple Diffusion : Simple diffusion allows the nonpolar and small molecules to pass through the plasma membrane without any assistance of proteins. In facilitated diffusion, larger polar molecules or ions move across the membrane through the help of transport proteins. Transport proteins are of two types, channel and carrier proteins. Channel proteins provide an open path for the molecules to move whereas carrier proteins hold the molecules to move across the membrane and change their shape.

Option A is correct answer.

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The astronaut gains a velocity of 4 m/s to the left.

What is Velocity?

The unit of velocity is meters per second (m/s) in the International System of Units (SI). Velocity can be positive or negative, depending on the direction of motion. A positive velocity means the object is moving in the positive direction, while a negative velocity means it is moving in the opposite direction.

According to the law of conservation of momentum, the total momentum of the system before the collision is equal to the total momentum after the collision, provided there are no external forces acting on the system.

Let's assume that the astronaut and the rock are initially at rest, so the total momentum before the collision is zero. After the rock is thrown to the right, the momentum of the system is:

P = m1 * v1 + m2 * v2

where m1 and v1 are the mass and velocity of the astronaut, m2 and v2 are the mass and velocity of the rock, and P is the total momentum.

Substituting the values given, we get:

P = 100 kg * v1 + 200 kg * 2 m/s

P = 100 kg * v1 + 400 kg*m/s

Since the total momentum of the system must be conserved, the total momentum after the collision must also be zero. Therefore:

P' = m1 * v1' + m2 * v2' = 0

where v1' and v2' are the final velocities of the astronaut and the rock, respectively.

We know that the rock gains a velocity of 2 m/s to the right, so its final velocity is v2' = 2 m/s. Substituting this into the above equation, we get:

100 kg * v1' + 200 kg * 2 m/s = 0

Solving for v1', we get:

v1' = -4 m/s

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Answer:

600 metres

Explanation:

1 minute = 60 seconds

1 second = 10 metres

60 seconds = 60 x 10 = 600

Athlete Mesert Defar runs 600 m in 1 minute. The speed of an object is equal to the distance traveled divided by time elapsed.

The speed of an object is equal to the distance traveled divided by time elapsed.

\(s = \dfrac dt \rm \ \ \ or\)

\(d = s \times t\)

Where,

\(d\) - distance

\(t\) - times = 1 minute = 60 sec

\(s\)  - speed = 10 m /s

Put the values in the formula,

\(d = 10 \times 60 \\\\ d = 600 \rm \ m\)

Therefore, Athlete Mesert Defar runs 600 m in 1 minute.

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Answer:

why is friction possible to slip on the wet floor​

Explanation:

This is because the coefficient of friction μ and the therefore resultant force of limiting friction Fs is significantly reduced when a lubricant is introduced between the the two kinetic or static surfaces.

Answer:

Pls mark me brainliest. the ans

Explanation:

Wet floors have less friction so there is a lesser chance of slipping. This is because the coefficient of friction μ and the therefore resultant force of limiting friction Fs is significantly reduced when a lubricant is introduced between the the two kinetic or static surfaces.

Answer:

1.Magnetic Force - Used in cranes to separate metal junk from junkyards.

2.Frictional Force- Helps us to walk.

Balanced forces do not change the motion of an object, Because the forces are the same size and acting in opposite directions.

Answer:

Balanced forces do not change the motion of an object. The motion of an object will not change if the forces pushing or pulling the object are balanced. An object that is sitting still will stay still if the forces acting on it are balanced.

Answer:

27.1m/s

Explanation:

Given parameters:

Height of the building  = 30m

Initial velocity  = 12m/s

Unknown:

Final velocity  = ?

Solution:

We apply one of the kinematics equation to solve this problem:

         v²  = u²  + 2gh

v is the final velocity

u is the initial velocity

g is the acceleration due to gravity

h is the height

          v²   = 12²  + (2 x 9.8 x 30)

          v  = 27.1m/s

Answer:

C. Photosynthesis

Explanation:

Photosynthesis is a process by which plants and photosynthetic bacteria obtain their food in presence of sunlight from water and carbon dioxide. They produce glucose as the food and oxygen is emitted as the byproduct. The equation for photosynthesis is - 6H2O+6CO2 → C6H12O6 + 6O2

Thus, the correct answer is 'C.Photosynthesis.'

The half-life of a first-order reaction is a constant that is related to the rate constant for the reaction: t1/2 = 0.693/k.

It is used in life-science laboratories in applications in which lower energy beta emissions are advantageous such as DNA sequencing. P can be used to label nucleotides. It is less energetic than 32P, giving a better resolution.

Phosphorus 33 is an artificial radioactive element. It is produced with a low yield by the neutron bombardment of phosphorus 31 (stable). The phosphorus 33 has a radioactive period of 25.3 days.

Phosphorus-33 atom is the radioactive isotope of phosphorus with relative atomic mass 32.971725, half-life of 25.34 days and nuclear spin (1)/2.

Phosphorus was discovered by the German merchant Hennig Brand in 1669.

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1 meter = 39.37 inches

Then the meter stick is 39.37 inches long.