According to the one-year calendar model based on the Big Bang theory, life on the planet began in __________.
December
August
January
September

Answer:

Explanation:

Given:

V₁ = V₂ = V

R₁ = 7 m

n = 7

R₂ = R₁ / n = 7 / 7 = 1 m

____________

aₙ₂ / aₙ₁ - ?

aₙ₁ = V₁² / R₁ = V² / 7

aₙ₂ = V₂² / R₂ = V² / 1 = V²

aₙ₂ / aₙ₁- =  V²  /  (V²/7) = 7

Centripetal acceleration increased by 7 times

The astronomer will take 0.086 hours to observe the radius of the black hole.

What is black hole?

In a black hole, the gravity is so intense that not even light can escape. The radius of black hole depends on the mass of the black hole.

The astronomer has determined a black hole's radius to be 51.0 au by examining its period of brightness variability.

The term "astronomical unit" (abbreviated "au") refers to a unit of length used to calculate the separation between the Earth and the sun.

1 au = 93 million miles.

Additionally, the radius is determined by the brightness variation, which takes the speed of light into account.

Light speed = 3 * [tex]10^8[/tex]m/s.

So,

time = distance / speed time

= 93 * [tex]10^9[/tex] / 3 *  [tex]10^8[/tex] time = 310 seconds.

1 second = 0.0002 hours.

310 seconds = 0.086 hours.

The astronomer will take 0.086 hours to observe the radius of the black hole.

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It will take 2.8 s  for the elevator to stop when it is moving with a speed of 2.5m/s

1)The cable will travel a linear distance equal to the distance covered by the elevator because it is constantly taut and neither slipping nor stretching.

2) Since the cylinder makes one full rotation, the cable's length is equal to the cylinder's circumference.

3) As a result, you must determine the cylinder's circumference, which is determined using the formula C = 2[tex]\pi[/tex] radius.

The radius is half the diameter: 1.2 m / 2 = 0.6 m

Hence, C = 2π × 0.6m = 3.8m

⇒ Distance run by the elevator = 3.8m

4) Now, assuming that the elevator decelerated uniformly from its starting speed of 2.7 m/s to a complete halt (Vf = 0), you use the related formulas:

i) [tex](V_{f})^{2}[/tex]= [tex](V_{o})^{2}[/tex] - 2ad ⇒ 2ad = [tex](V_{o})^{2}[/tex]- [tex](V_{f})^{2}[/tex] ⇒ a = [tex](V_{0})^{2}-(V_{f})^{2}[/tex]/ (2d)

a = [2.7 m/s]² / (2×3.8m) = 0.96 m/s²

ii) [tex]V_{f}[/tex] =  [tex]V_{0}[/tex]- at ⇒ t = [2.7 m/s] / (0.96 m/s²) = 2.8 s

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Answer: Since the ball is free-falling, you use this equation:

v^2 = 2gh

where v is the velocity

g is the acceleration due to gravity

h is the height at which the object is dropped from

Plugging in the values and converting ft to m,

v^2 = 2 (9.8) (12) (0.3)

v = 8.4 m/s

The power supplied to the household washing machine connected to the 223 V source is 223 W.

Current = I = 1 A

Voltage = V = 223 V

We have to calculate power supplied to the household washing machine,

Power = P =

= Power = Voltage X Current

= P = V X I

= P = 223 X 1

= P = 223 Watt

Power is the amount of energy transferred or converted per unit time.  

Thus, the power supplied to the washing machine by the source of 223 V which draws 1 A of current is 223 W.

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When the two blocks touch each other, both blocks will have the same temperature and it will be closer to 0 degrees Celsius than 84 degrees Celsius.

option A is the correct answer.

The final temperature of the blocks or the equilibrium temperature of the blocks when they touch each other is determined by applying the principle of conservation of energy as follows;

Heat lost by the smaller block = Heat gained by the bigger block

m₁c(T₁ -T) = m₂c(T - T₂)

where;

m₁(T₁ -T) = m₂(T - T₂)

5 x (84 - T) = 50(T - 0)

420 - 5T = 50T

420 = 55T

T = 420/55

T = 7.64⁰C

Thus, we can conclude that both blocks will have the same temperature which will be closer to 0 degrees Celsius than 84 degrees Celsius.

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A current flows down a vertical wire in a straight line.  Using right hand thumb rule,the magnetic field is directed southward to the east of this wire.

Define right hand thumb rule ?      

The relationship between the movements of the magnetic field surrounding a specific conductor and its current direction can be found in a straightforward manner. This method would be known as the right-hand thumb rule. According to the right-hand rule, the magnetic field lines produced by a wire carrying current may be oriented in a manner similar to that of a person's right hand's folded fingertips, with the thumb pointing in the direction of the current flow.

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Answer: To raise the temperature of 0.6 kg of water by 60k 4200jkg-¹c-¹

Reason:

Using the formula Pt = (4.2 × L × T ) ÷ 3600 you can calculate the time it takes to heat a specific quantity of water from one temperature to another temperature.

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Electrostatic potential energy overall The unit of this charge system is -6.71kq2/d.

Who was the first to define energy?

The term "energy" was originally used in the field of science by Thomas Younger in 1800, but it did not catch on. Young later used interfered experiments to prove that light is a wave.

Briefing-

The expression for the electric potential energy is,

U= k*q1q2/d

The electric potential energy due to charges +2q and +5q is,

U25=k*(10q2)/d

The electric potential energy due to charges +2q and +q is,

U21=k*(2q2)/d

From the above figure, the distance between charges +2q and -3q is

√d² +√ d² = √2d²

= √2d

The electric potential energy due to charges +2q and -3q is,

U23=-k(6q2)/√2d

Thus, the total electric potential energy of the system is,

Utot=U25 +U21+U23 +Us1+U53 +U31

=k*(10q²)/d+k*(2q²)/d-k*(6q2)+k* (5q2)/√2d + k (10g2)/√2d

-k. (15q2)/d-k(3q2)/d

= [10+2-6/√2 + 5/√2 -15-3]kq2/d

=-6.707 kq2/d

=-6.71kq2/d

Utot=-6.71kq2/d =(approximately)

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The complete question is-

Four point charges form a square with sides of length dd, as shown in the figure. In the questions that follow, use the constant k in place of 1/4πϵ0.

Part A: What is the electric potential Vtot at the center of the square? Make the usual assumption that the potential tends to zero far away from a charge. Express your answer in terms of q, d, and appropriate constants.

Part B: What is the contribution U2q to the electric potential energy of the system, due to interactions involving the charge 2q? Express your answer in terms of q, d, and appropriate constants.

Part C: What is the total electric potential energy Utot of this system of charges? Express your answer in terms of q, d, and appropriate constants.

The maximum height above the point of release that the block reaches as it oscillates is 0.0385 m and the spring constant is  6.63 N/m.

Simple harmonic motion (SHM) is a type of periodic motion or oscillation motion that is a repetitive motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement from an equilibrium position

a) The force exerted by the spring (F) is given by Hooke's law as:

F = -kx

where, k is the spring constant.

At equilibrium, the weight of the block is balanced by the force of the spring, so we have:

mg = kx

where, g is the acceleration due to gravity.

Substituting the given values, we get:

k = mg/x = 0.428 kg * 9.81 m/s² / 0.626 m = 6.63 N/m

b) The period of oscillation of the block (T) is given by:

T = 2π√(m/k)

Substituting the given values, we get:

T = 2π√(0.428 kg / 6.63 N/m) = 0.668 s

c) The maximum height above the point of release (h) can be found using the conservation of energy principle. At the point of release, the block has a potential energy of mgy and no kinetic energy. At the maximum height, the block has a kinetic energy of (1/2)mv² and no potential energy. Therefore, we have:

mgy = (1/2)mv²

Solving for h, we get:

h = y - v²/2g

where, v is the velocity of the block at the point of release.

The velocity of the block can be found using the conservation of mechanical energy principle as:

(1/2)k(y + x)² = (1/2)mv²

Substituting the given values, we get:

v = √[(k/m)(y + x)²] = √[(6.63 N/m / 0.428 kg)(0.365 m + 0.626 m)²] = 0.772 m/s

Substituting v into the equation for h, we get:

h = 0.365 m - (0.772 m/s)² / (2 * 9.81 m/s²) = 0.0385 m

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The friction force the brake pad applies to the shaft f = 0.34 N.

Solution:

∝ = Rf sin∅

(-3.05 x 10⁻³) = (9 x 10⁻³) f sin(-90°)

f = 0.34N

As the two surfaces slide over each other small ridges are pressed against each other. Friction creates a force on a surface that opposes its motion. Friction can be reduced by applying lubricant. Friction is a type of contact force. It exists between tangent faces.

Friction is the force the resistance to movement when one object rubs against another. Friction occurs when two objects rub against each other. Friction works against the motion and works in the opposite direction. The amount of friction depends on the materials that make up the two surfaces.

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Tension must the string be placed is 86.75 N.

What is Tension?

In physics, tension is defined as the pulling force that is transmitted axially by a string, rope, chain, or similar object, or by each end of a rod, truss member, or other comparable three-dimensional object. Tension can also be defined as the action-reaction pair of forces acting at each end of the aforementioned elements.

f = 440 Hz

l = 32 cm = 0.32 m

m = 0.35 g = 0.35 x 10^-3 kg

μ = m / l = 0.35 x 10^-3 / 0.32 = 1.094 x 10^-3 kg/m

The formula for the fundamental frequency is given by

[tex]f=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}$$[/tex]

Where, T be the tension

[tex]$$\begin{aligned}& 440=\frac{1}{2 \times 0.32} \sqrt{\frac{T}{1.094 \times 10^{-3}}} \\& 281.6=\sqrt{\frac{T}{1.094 \times 10^{-3}}}\end{aligned}$$[/tex]

T = 86.75 N

Thus, the tension in the string is 86.75 N.

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The speed of light in vacuum is(3*10^8 m/s).

What is speed?
The speed of an object, also known as v in kinematics, is the size of the change in that object's position over time or even the size of the change in that object's position per unit of time, making it a scalar quantity. The initial speed is the upper limit of a average speed as that of the duration of a time interval gets closer to zero. The average speed of the object in a period of time is indeed the distance travelled by object divided by duration of the interval. Velocity and speed are not the same thing. The dimensions of speed are time divided by distance.

The velocity of the light in the material is 0.2c, where c is the speed of light in vacuum (3*10^8 m/s).

The frequency of the light in the material is equal to the frequency of the light in vacuum divided by the index of refraction, which is equal to (3*10^8 m/s) / 50 = 6*10^6 m/s.

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This bifurcation is called a saddle-node bifurcation. In it, a pair of hyperbolic equilibria, one stable and one unstable, coalesce at the bifurcation point, annihilate each other and disappear.

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Answer:

21.6 m/s

Explanation:

To solve this problem, we can use the principle of conservation of momentum. This principle states that the total momentum of a system remains constant unless an external force acts on it. In this case, the only external force acting on the system is the collision force between the two cars, which causes the cars to stick together and move as a single unit.

The initial momentum of the first car is 1750 kg * 23 m/s = 40250 kgm/s. The initial momentum of the second car is 1500 kg * 20 m/s = 30000 kgm/s. The total initial momentum of the system is 40250 kgm/s + 30000 kgm/s = 70250 kg*m/s.

After the collision, the two cars move together as a single unit, so the total mass of the system is 1750 kg + 1500 kg = 3250 kg. Since the total momentum of the system remains constant, the final velocity of the combined cars must be 70250 kg*m/s / 3250 kg = 21.6 m/s.

In summary, the two cars move together at a velocity of 21.6 m/s immediately after the collision.

Answer:

Approximately [tex]2.1 \times 10^{3}\; {\rm m}[/tex] ([tex]2.1\; {\rm km}[/tex]) assuming that the speed of sound in the water is [tex]1482\; {\rm m\cdot s^{-1}}[/tex] ([tex]20\; ^{\circ}{\rm C}[/tex].)

Explanation:

Multiply speed [tex]v[/tex] by time [tex]t[/tex] to find the distance [tex]s[/tex] travelled.

The sound wave in this question has travelled a distance of at least:

[tex]\begin{aligned}s &= v\, t\\ &= (1482\; {\rm m\cdot s^{-1}})\, (2.8\; {\rm s}})\\ &\approx 4.15\times 10^{3}\; {\rm m}\end{aligned}[/tex].

Note that this distance is for a round trip- from the ship to the ocean floor and back. The depth of the ocean at this location will be one-half the distance of a round trip:

[tex]\begin{aligned} \frac{4.15\times 10^{3}\; {\rm m}}{2} \approx 2.1\times 10^{3}\; {\rm m} = 2.1\; {\rm km}\end{aligned}[/tex].

The minimum amount of force (famin) required to keep the box from sliding down the hill depends on several factors, such as the angle of the hill, the size and weight of the box, and the type of surface the box is sitting on.

What is force?
A force is indeed an influence that really can alter an object's motion according to physics. A force may cause an object to mass to accelerate when it changes its velocity, such as when it moves away from rest. An intuitive way to describe force is as a push or even a pull. A force is a vector quantity because it has both direction and magnitude. It is calculated using the newton SI unit (N). Force is denoted by the letter F. (formerly P). The net force acting on an object seems to be equal to the speed that its momentum changes over time, according to Newton's second law in its original formulation.

Generally, the more inclined the hill, the more force you will need to apply. If the box is light and the surface is slippery, you may need to apply more force to keep it from sliding. The best way to determine the exact amount of force necessary is to experiment and adjust the amount of force as needed.

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Most are unchanged since their formation in the solar nebula are common in asteroids and comets.

The asteroid belt, a region of the solar system between Mars and Jupiter, is where asteroids are most frequently found. The first asteroids were not found until the beginning of the nineteenth century; they are too small to be seen without a telescope.

A number (corresponding to the order of discovery) and occasionally a name are assigned to asteroids. At first, goddesses from Greek and Roman mythology were used to name asteroids. Astronomers turned to the names of colleagues (and other notable people) they wished to honor after exhausting these and other female names (including, later, those of spouses, friends, flowers, cities, and others). For instance, Morrison, Fraknoi, and Sidneywolff are the names of asteroids 2410, 4859, and 68448 respectively.

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The force constant is 2.145 N/m.

Using the relation;

T = 2π√m/k

T = time period = 0.45 s

m =  mass of object in kilograms = 0.011kg

k = spring constant

To find k based on the formula,

k = 4 × (3.142)^2 × 0.011 / (0.45 )^2

k = 2.145 N/m

Therefore the force constant is 2.145 N/m.

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To reduce the resonant frequency of a mass, I would b)increase the mass .So, correct option is b.

A thunderous recurrence is the normal vibrating recurrence of an item and indicated as 'f' with an addendum zero (f 0). At the point when an item is in balance with acting powers and could continue to vibrate for quite a while under wonderful circumstances, this peculiarity is reverberation.

We know very well that resonant frequency of simple harmonic motion system is given by 2π√k/m where k is spring constant and m is the mass of the body,

Now, we can see that frequency is inversely proportional to mass and directly proportional to spring constant.

Now, on increasing the spring constant we can see that resonant frequency will also rise.

On increasing the mass of the body resonant frequency will decrease since resonant frequency is inversly proportional to mass.

Increasing the damping will not effect the resonant frequency since frequency does not depend on the material of the body.

Hence, option b is correct.

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(Complete question) is:

Suppose that you wanted to reduce the resonant frequency of a mass and spring harmonic motion system, what could you do?

a)increase the spring constant

b)increase the mass

c)decrease the spring constant

d)increase the damping.

The energy of the least energetic photon that can be absorbed by these atoms when initially in their ground state is numerically equal to energy of the electron at that orbit.

In chemistry and atomic physics, an electron shell—also known as a fundamental energy level—is the orbit of one or more electrons around the atomic nucleus. The shell that is closest to the nucleus is the "1 shell," often referred to as the "K shell."

The shells that are farther and farther away from the nucleus are the "2 shell," also known as the "L shell," "3 shell," also known as the "M shell," and so on. Either the main quantum numbers (n = 1, 2, 3, 4) or the X-ray notation letters are used to designate the shells (K, L, M, N...).

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The ratio of the skater's moment of inertia when they have their arms extended to when their arms are not is r²/(r+r₁)².

The moment of inertia of any particular object can be defined as the opposition displayed by the object in question whenever its speed of rotation is changed when any external(turning) force is applied.

Let us assume that the moment of inertia of the skater when they don't extend their arms be = mr² (i)

Here, r is the radius of their body with their arms squeezed in.

The moment of inertia when the skater will extend their arms outwards is going to be = m(r+r₁)² (ii)

Here, r₁ is the radius of the hands when they are extended.

Comparing and equating (i) and (ii), we get -

Ratio =  r²/(r+r₁)²  (m is common for both so it gets canceled)

Henceforth, here is the ratio for when the skater has their arms extended to when their arms are not.

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The work done in by the attendant on a can of soup is 2.3 J.

What is Work in physics?

Work in physics is defined as the dot product of force and the displacement produced by it.

Given is an attendant who pushed 0.450 m horizontally with a force of 5.10 N.

From the definition of work done, we can write -

W = F.d

W = Fd cosФ

Then angle between force and displacement is 0°. Therefore, cosФ is equal to 1.

Work = Fd

Work = 5.10 x 0.450

Work = 2.295 joules = 2.3 J

Therefore, the work done in by the attendant on a can of soup is 2.3 joules.

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The "sum of the product of mass" of each particle with the "square of its distance from the axis of rotation" is the formula for the moment of inertia.

The term "moment of inertia" refers to the quantity that describes how a body resists angular acceleration and is calculated by multiplying each particle's mass by its square of distance from the rotational axis. The sum of the moments of inertia about any two mutually perpendicular axes lying in the plane and passing through the given axis determines the moment of inertia (MI) of a plane area about that axis.

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The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity.

It's SI unit is m/s^{2}. It is of vector nature which includes both magnitude and direction makes it a quantity. The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/s^{2}.

Acceleration due to gravity, acceleration of gravity or gravity acceleration may refer to:

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The motion of the water atoms in a wave is orbital. When the depth exceeds 50% of the wave's wavelength, the wave is said to be in deep water.

Wavelengths vary wildly between different types of waves. Surf waves in the ocean have a wavelength of 30–50 m, but tsunamis have significantly longer wavelengths (about 100km). Humans can hear sounds with wavelengths between 70 mm and 70 m, depending on the pitch of the sound.

The medium (such as air, water, or a vacuum) through which a wave travels determines its wavelength. The periodic electrical signals in a conductor, sound waves, light waves, and water waves are all examples of waves.

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A projectile's range is the horizontal distance it has traveled.

x = V * t  x = V * t can be used to calculate horizontal distance.The formula y = - g * t2 / 2 describes vertical distance from the ground, where g is the acceleration of gravity and h is an elevation.

An illustration of a horizontal distance is the space between a building and the observer, while an illustration of a vertical distance is the height of the building.

The range is the horizontal distance from the launch position to the landing place.An angled-launch projectile's range is influenced by its launch speed and angle .

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Diameter will be 1.8914m

The Rayleigh criteria, which is given by the equation θ = 1.22 λ/D, yields the best resolution or shortest angle between point sources. Once this angle has been determined, it is possible to determine the distance between stars since we already know how far away they are.

In our case,

λ = 4.0 cm.

sin(θ) ≈ tan(θ) ≈ θ = y/D = 31/1200 ≈ 0.0258

According to Rayleigh's criterion,

R = 1.22 λ/D = 1.22 * 4.0 * 10-2 / D = 0.0258

∴  D = 1.22 * 4.0* 10-2 / 0.0258 m ≈ 1.8914m.

D = 1.8914m

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The location of its image in rel-ation to the mirror is -2.5 m

Given that, an object placed 45.0 cm from a concave mirror having the focal length of 15.0 cm and height of image is 5.0 cm.

We have to find the image distance (v) from the mirror and height of the image (h).

From above data we have, focal length (f) of concave mirror is -15 cm, object distance (u) is -45 cm and height of image (h) is 5 cm.

Now, Using Mirror Formula

1/f = 1/v + 1/u

Where f is focal length, v is image distance from the mirror and u is object distance from the mirror (concave).

The known values in the above formula to find the value of 'v' i.e. image distance from the mirror.

1/(-15) = 1/v + 1/(-45)

-1/15 = 1/v1 - /45

-1/15 + 1/45 = 1/v

(-3+1)/45 = 1/v

-2/45 = 1/v

-45/2 = v

-22.5 = v

Therefore, the image distance from the concave mirror is -22.5 cm.

Now,

m = -v/u = h/h•

Replace the values,

-(-22.5)/(-45) = h/5

-0.5 = h/5

-2.5 = h

Hence, the location of its image in rel-ation to the mirror is -2.5 m

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