what is the length of a pendulum whose period on the moon matches the period of a 2.8- m -long pendulum on the earth?

Objects such as the Great Nebula in Andromeda were once called extragalactic nebulae. It is now realized that they are actually.

Extragalactic systems are systems containing objects that lie outside the Milky Way. The branch of astronomy that deals with this massive region of space is called Extragalactic Astronomy. In other words, it is the polar opposite of Galactic Astronomy.

Astronomers believe they've spotted the first extragalactic exoplanet beyond our own galaxy. Residing some 28 million light-years away near the heart of the Whirlpool Galaxy (M51), the binary system M51-ULS-1 consists of either a neutron star or a black hole that's tangoing with a more standard companion star.

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1.2s is the period of oscillation of a disk is suspended by a nail such that it pivots in a vertical plane about a point on the edge of the disk when the disk's radius is given 25 cm.

The period, what is known as the length of each full oscillation, is constant. T = 2 Square root of L/g, where L is the pendulum's length and g is the acceleration brought on by gravity, is the formula for a pendulum's period.

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5.94 ×10-26 J of energy of photons of radio waves is required to leave an FM station having 90MHz broadcast frequency

A photon's energy E and frequency f are exactly related. This is expressed mathematically as

Equation

E=hf      (1)                       

where h is the Planck constant.

Given that the frequency of the radio wave is f=90 MHz

=9.0×107 Hz

and knowing the fact that the numerical value of Planck's constant is h=6.6×10−34 m-m-kg/s

then the energy of the photon in J using Eq. (1) is:

E=6.6×10−34× 9×107

E=5.94 ×10-26 J

what is Frequancy?

The frequency of a repeated event is its number of instances per time unit.   It differs from angular frequency and is sometimes referred to as frequency for clarification. The unit of frequency is hertz (Hz), or one occurrence per second. The duration is the inverse of frequency since it is the amount of time that passes between events.

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Factor that does not significantly affect the amount of solar energy reaching the surface of earth is : distance between earth and sun.

Solar radiation that reaches surface of the Earth without being diffused is called direct beam solar radiation. Sum of the diffused and direct solar radiation is called global solar radiation.

Rotation of earth also does not affect the amount of solar radiation received at the Earth's surface. Tilt, orientation, latitude, and climate can have great impacts on a solar system's performance.

Solar energy is generated by the nuclear reaction within the sun and this energy reaches the surface of the earth in the form of electromagnetic radiation.

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"While Kendall is accelerating and Gabriella was slowing down in lockstep, Franklin is not doing so.

When an object accelerates, its acceleration also moves in the same direction as its velocity. This indicates that the situation is developing. Example B shows an object moving in reverse while accelerating (i.e., having a negative velocity).

By dividing that velocity change but by time it takes for change to occur, acceleration is determined. Similar to velocity, acceleration has a direction. When something speeds up, it moves more quickly in the area it is moving.

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The magnitude of the electric field will be greater where the lines of the charges are closest to each other.

An electric field is defined as an area that holds the electrically charged particles in its physical field and the electric field also exerts a force on all charged particles either attracting them or repelling them. If the force that is exerted on the charged particle varies from one point in the field to other then the electric field is said to be non-uniform.

In opposite charges, zero is not a possibility between two charges because the field vectors from both opposite charges will head toward the negative charge.

So we can conclude that the point where the field is zero does not exist.

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The amount of heat that  is dropped in the hot reservoir is equal to 100 J. Option A

According to the first law of thermodynamics, we know that energy can neither be created nor destroyed but can be converted from one form another.  

We can see that as the heat is transferred from the we do some work so as to be able to extracts heat from a cold reservoir and dumps heat into a hot reservoir. Since heat can neither be created nor destroyed, the heat that is dumped must be equal to the amount of heat that is extracted.

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A block is attached to a spring is oscillating with an amplitude of 10 cm. If its total energy is quadrupled, the amplitude of resultant periodic motion becomes 16 times.

The position of block over time is given by the equation:

x(t) = A cos(ωt + Ф)

where, A is the amplitude

ω is the angular frequency

Ф is the angle

The total energy of the oscillation or periodic motion is stored as the potential energy. It is given by the equation, E = 1/2 * k * x²

where, k is the spring stiffness

Hence, the total energy is directly proportional to the square of the amplitude.

E ∝ A²

which means that, if energy is doubled the resultant amplitude of the periodic motion is 2² of quadrupled.

Similarly, if the total energy is quadrupled, the amplitude will be 4² times or 16 times.

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The relationship between wave characteristics and the generation of electrical energy is that energy of the wave is converted into electrical energy and the energy carried by this wave depends on its amplitude.

The average power of a wave is the amount of energy of the wave transmitted over a given time.

Power = energy / time

The amount of energy carried by a wave is related to the amplitude of the wave.

A high energy wave is characterized by a high amplitude; a low energy wave is characterized by a low amplitude.

Mathematically, the formula for the average power of a wave is given as;

P(avg) = ¹/₂μω²A²v

where;

Thus, the energy carried by a wave is a function of its amplitude and speed.

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The gravitational force of the Earth is 686N.

Gravitational force is a very long-range, but relatively weak fundamental force of attraction that acts between all particles that have mass; believed to be mediated by gravitons.

The equation to calculate gravitational force is as follows:

F = Gm₁m₂/r²

Where;

F = 6.674 × 10-¹¹ {5.98 × 10²⁴ × 70}/(6.38 × 10⁶)²

F = 6.674 × 10-¹¹ {4.186 × 10²⁶ ÷ 4.07 × 10¹³}

F = 6.674 × 10-¹¹ {1.03 × 10¹³}

F = 6.86 × 10²

F = 686N

Therefore, 686N is the gravitational force.

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The length of the aluminum flagpole will increase by 0.00881 m as the temperature increases by 15.

The length of an aluminum flagpole may not change with temperature. While thermal expansion can cause materials to change in size when heated or cooled, aluminium, as a metal, is not significantly affected by temperature changes. As such, the length of an aluminium flagpole is unlikely to be significantly affected by changes in temperature.

Calculate the Coefficient of Linear Expansion for Aluminum

The coefficient of Linear Expansion for aluminum is about 0.000023 per degree Celsius

Calculate the change in length

Change in length = (Coefficient of Linear Expansion x Original Length x Change in Temperature)

Change in length = (0.000023 x 39.4 m x 15) = 0.00881 m

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Answer: Fa = 52,5N

Explanation: The force that causes an object to move is called Force of application which is calculated by the formula Fa = m × a (Force of application = mass multiplied by the acceleration)

=> Fa = m × a

Fa = 35kg × 1.5m/s²

Fa = 52.5N

A diode is a two terminal device that passes and blocks the current.

A diode is a semiconductor gadget that essentially switches current in a single direction.

However, it substantially inhibits current flow in the opposite direction. It permits an easy flow of current in one direction.

Due to the fact that they convert alternating electricity into pulsing direct current, diodes are sometimes referred to as rectifiers. Type, voltage, and current capability are used to rate diodes.

The anode and cathode determine the polarity of diodes. The majority of diodes only permit current to flow when the anode is subjected to positive voltage.

A diode is forward-biased when it permits current flow. Reverse-biased diodes function as insulators.

The arrow of the diode symbol points away from the direction of electron flow. The symbol was created by engineers, whose current flowed in a positive direction.

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Answer:

All its mass makes a combined gravitational pull on all the mass in your body.

Explanation:

Basically anything with mass has gravity

Regarding the masses of antimatter particles, the true statement is: A. The mass of an antimatter particle is the negative value of that of its corresponding matter particle.

Matter is any substance made up of particles that takes up space by their volume and also have mass. Meanwhile, antimatter is a particle made up of antiparticles of the corresponding ordinary particles. One of the differences between matter and antimatter is the charge of their mass. An antimatter has the opposite electric charge of its corresponding matter. So, it is safe to say that the mass of an antimatter particle is the negative value of its corresponding particle.

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The magnitude of force exerted by the rope on the crate is 312 N.

From Newton's second law of motion, we know the expression of force as,

F = m * a

where, m is mass

a is acceleration

Given that, mass of the crate is 40 kg

Acceleration is 2 m/s²

The net force that the rope is applying to the card while it is sliding downward is given by,

F = m(g - a)

Substituting the values,

F = 40(9.8 - 2)

F = 312 N

Thus, the net force exerted by the rope on the crate is 312 N.

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An object weighing 5 kg is perched on a smooth incline that slopes at a 26-degree angle to the horizontal. The amplitude of the object's acceleration is given by F>mg sin26.

The rate where the direction of movement change over time is referred to as acceleration. Anything is said to be rushing when that goes faster or slower.

The three main types of propelled motions are regular accelerated, non-uniform velocity, and points of data. The motion in which an item moves in a single direction while increasing in velocity at regular intervals is referred to as uniform acceleration.

F = ma

F - mg sin26 = ma

a = F - mg sin26/m

a = F/m - gsin26

which implies, F>mg sin26.

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The above statement states that when the minimal angle of departure is 29 degrees, then index of refraction is 1.26.

Refraction occurs when light bends or changes direction as it passes through one material and then another. For instance, when light strikes water after passing through the air, it refracts. As a result, the straw in a water glass may appear bent at the water's surface. Some surfaces don't refract or reflect light at all.

D=29°

As for the refractive index:

μ=2sin(30°+D/2)

  =2sin(30°+29°/2)

  =2sin(30°+14.5°)

  =2sin(44.5°)

  =2*0.63

  = 1.26

Therefore the refractive index is 1.26.

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Answer:

First, write the velocities in component f…

Explanation:

As per as calculations

80 kilometers east in two hours in a car. The car has a westward speed is 40 km/h.

The vector illustration expression of velocity is the movement in space-time of an object or particle. The recognized unit of velocity magnitude is the centimeter per second (m/s) (also known as speed).

Speed is the rate at which an object is moving across a path over time, whereas velocity is the speed or direction that an organism is moving. In other words, velocity is a scalar value, but velocity is a vectors.

An object's velocity is a vector quantity. Both magnitudes and direction are present.

Arrows serve as directional indicators.

Car A is traveling west. Moving in an east-south direction is Car B. Vehicle C is traveling in a southerly direction. Vehicle E is traveling in a northerly direction.

Therefore, the Car is moving west at a speed of 40 km/h.

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The amount of heat generated for each cylinder height is found out to be

100 m : 4.9 kJ

200 m : 9.8 kJ

1000 m : 49.1 kJ

In order to calculate this, you just have to calculate the PE of every cylinder and formula for PE is:

PE = g* h* m

where, m is mass

h is height

g is gravity

So, we just have to insert the values into the formula, to obtain results.

For 100m cylinder, PE = g* h* m

PE = 9.8* 100* 5 = 4900 J = 4.9 kJ

For 200m cylinder,

PE = 9.8* 200* 1 = 9800 J = 9.8 kJ

For 1000m cylinder,

PE = 9.8* 1000* 1 = 49100 J = 49.1 kJ

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The final velocity of the rugby player is 15.62m/s.

Acceleration is the rate of change in both speed and direction of velocity over time. When something moves faster or slower in a straight line, it is said to have been accelerated.

Meter per second per second (m/s2) is the unit of acceleration. Definition. The force known as the snewton is that which, when applied to a mass of one kilogram, results in an acceleration of one metre per second per second.

Given,

Initial velocity u = 2m/s

distance s = 20 m

acceleration a = 6 m/s

v² = u²+ 2as

v² = 2² + 2×6×20

v² = 4+240

v² = 244

v = √244

v = 15.62m/s.

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Complete question is "A rugby player is moving at an initial speed of 2 m/s and takes a distance of 20 m to accelerate to 6 m/s. Calculate the final velocity of the rugby player."

Advantages of simplifying combinational logic circuits:

1. Simplified uses fewer gates to provide the same logic properties as necessary.

2. A circuit with fewer gates is smaller and less expensive than an original.

3. Because there are fewer interconnections, the reliability of the circuit will increase.

4. The circuit's operating speed goes up.

5.There are no redundant gates because of the simplification.

How simplifying combinational logic circuits make designs more efficient and beneficial to society?

It is challenging to design a circuit if it is complex, so the circuit should be as basic as feasible before design. We may need to provide a less amount of power if there are more gates. Therefore, combinational logic circuit simplification is good for society.

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In the given explanations, Newton’s law of universal gravitation can be explained by the statement, "Heavier objects fall faster than lighter objects". Thus, Option A is the correct answer.

Gravity is a natural phenomenon that causes all massive objects to attract each other. The magnitude or force of this interaction depends on the masses and distance of the bodies. This causes objects to fall toward Earth, for example, and keep satellites and celestial bodies in their orbits, such as the Earth's orbit around the Sun. Gravity also causes the tidal phenomenon.

In physics, gravity can be approximated by Isaac Newton's laws of gravity. Although the accuracy of the law is sufficient, for example, when calculating the orbits of spacecraft, gravity is best described by Albert Einstein’s general theory of gravity, in which it is considered the curvature of space-time.

Newton's law of universal gravitation states that a particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Hence, Option A is the correct answer.

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The distance can be calculated as 490m .

We are given that,

Time = t = 10s

Initial velocity = u = 0

Acceleration due to gravity= g = 9.8m/s²

Suppose v is the final velocity. Where "t" stands for time, "s" for distance, "u" for starting velocity, and "g" for the acceleration brought on by gravity. Currently applying the second Newtonian equation for motion,

s = ut + 1/2 gt²

Putting the values in above equation ,

s = 0 + 1/2 (9.8)(10)(10)

s = 1/2 × 980

s = 450m

In this case, the distance is 490 m.

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The greatest possible angular speed an object can have is 46072.3431  rad/s.

Any two objects with mass are drawn together by the gravitational force. The gravitational force is known as. According to F=Gm₁m₂/r², the direction of force will always point in the direction of the opposing mass along the line connecting the two bodies. It is an alluring natural force.

The gravitational force will balance the centripetal force,

GmM/R² = mRω²

ω = √GM/R³

ω = √6.67 × 10⁻¹¹ × 2 × 1.989×10³⁰/5000³

ω = √2.653×10²⁰/5000³

ω = √2.653×10²⁰/1.25×10¹¹

ω = √2.122×10³¹

ω = 46072.3431 rad/s.

The greatest possible angular speed an object can have is 46072.3431  rad/s.

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Answer:

SUV's velocity is 22 m/s

Explanation:

[tex]F=\frac{mv^{2} }{r} \\\\v=\sqrt{\frac{Fr}{m} } \\\\v=\sqrt{\frac{14236 N * 85 m}{2500 kg} } \\\\v=22 \frac{m}{s}[/tex]

a).  the rocket's maximum altitude is 54.8km .

b). the rocket in the air 227.6 s

Calculation :

Given data

The expression from the equation of motion can be given as,

v₁²−v²=2gs1......(1)

The velocity during the first phase can be calculated as,

v1=vo+at1

v1=0+(30×30)

v1=900m/s

(a)

The altitude attained during first phase can be calculated as,

s1=v²₁ / 2a

s1=900/(2×30)

s1=13500m

Substituting the values in equation 1 for distance travelled during second phase,

(900)²−0=2×(9.8)×s₂

s2=41326.5m

The maximum altitude attained by rocket can be calculated as,

s=s1+s2

s=13500+41326.5s

=54826.5m

s=54.8km

(b)

The total time period can be calculated by the expression,

t=ta+td......(2)

The time taken in second phase of the motion can be calculated as,

v=v1+gt2

0=900−(9.8)t2

t2=91.8s

The time of ascent can be calculated as,

ta=t1+t2

ta=30+91.8

ta=121.8s

The time of descent can be calculated as,

td=√(2s/g)

td=√(2×54832.5)/(9.8)

td=105.8 s

Substituting the values in equation 2,

t=121.8+105.8

t=227.6 s

Thus, the duration of rocket in the air was 227.6 s

(c)

Figure

From the figure,

At point A, fuel was out.

At point B, rocket attended maximum altitude.

At point C, rocket fell on ground.

Acceleration is the rate of change of an object's velocity with respect to time. Acceleration is a vector quantity (as long as it has magnitude and direction). The direction of an object's acceleration is given by the direction of the net force acting on that object. As described in Newton's second law the magnitude of an object's acceleration is the combined effect of two sources.

The mass of this object is inversely proportional to the mass of the object, depending on the material from which it is made.

The SI unit of acceleration is meters per second squared.

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As a result of the expansion, parallax method is the way to compare the average distances between galaxies in the distant past and average distance between them today

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