8) A simple pendulum consisting of a 20-g mass has initial angular displacement of 8.0°. It oscillates with a period of 3.00 s(a) Determine the length of the pendulum.(b) Does the period of the pendulum depend on the initial angular displacement?
(c) Does the period of the pendulum depend on the mass of the pendulum?
(d) Does the period of the pendulum depend on the length of the pendulum
(e) Does the period of the pendulum depend on the acceleration due to gravity?

Revolutions made by the blade will be 266 rev

Given:

Constant angular acceleration = 0.82 radians/second^2

number of revolution per minute = 500

To Find:

number of revolution

Solution: Angular Acceleration is defined as the time rate of change of angular velocity. It is usually expressed in radians per second per second.

Initial speed of the helicopter blade, w₁ = 0

The final speed of the blade, wf = 500 rpm = 500 x 2π/60 rad/s = 52.35 rad/s

We need to find the number of revolutions. Firstly we will find the angle turned by the blade. Let the angle is θ

So,

wf^2 - wi^2 = 2αθ

θ = wf^2/2α = 1671 rad

Let there are n number of revolutions made by the blade. So,

n = θ / 2π

n = 1671 / 2 x 3.14 = 266 rev

So, the revolutions made by the blade will be 266 rev

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The nucleus that completes the equation given above is 218/85 At, which is option D.

Nuclear fission is a nuclear reaction in which a large nucleus splits into smaller ones with the simultaneous release of energy.

According to this question, the following nuclear fission reaction is given: 222/87Fr = 4/2He+ ?

To find the missing nucleus, we subtract 4 from 222 to get 218, therefore, the nucleus that completes the equation given above is 218/85 At.

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The total distance the toy car traveled is D. 19cm

The total distance of the toy car traveled in cm would be calculated

We would add the sum:

D = 9 + 4 + 6 cm

D = 19 cm

Therefore, the total distance the toy car traveled in cm is 19 cm.

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Mass is the same, weight is less

As we know that the mass of the object is the measurement of the quantity of the matter that is present in it

So here we can say that if the mass of the object is m then its total quantity of the matter that is present in it is given as

mass = (density) × (volume)

Now for the weight of the object is defined as the force of gravity due to planet

Fg = mg

so the weight of the object is depending on the acceleration due to gravity of the planet

As we know that the gravity of moon is smaller than the gravity of the earth so here weight on the moon will be smaller than the weight on the Earth

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At the time of quark confinement, when the universe was 10-6 seconds old, there is found to be one additional proton for every billion antiprotons.

Note that  one quark is never found on its own but if particles are said to be smashed together and quarks are found, they are said to be like ends of rubber bands that expands.

Hence, At the time of quark confinement, when the universe was 10-6 seconds old, there is found to be one additional proton for every billion antiprotons.

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Answer:

2.72×10^-7

Explanation:

velocity = frequency × wavelength

2.05×10^8=7.55×10^14 wavelength

wavelength = 2.05×10^8/7.55×10^14

wavelength = 2.72×10^-7

The angle between the two vectors is 0⁰, thus the two vectors are parallel to each other.

The angle between the vectors describes the direction of the vector and the value of the angle can be determined from the horizontal and vertical components of the vectors as shown below.

The sum of the horizontal components and vertical components of the vectors is calculated as follows;

Sum of the horizontal component of the vectors, x = 1 + 1 = 2

Sum of the vertical component of the vectors, y = -1 + 1 = 0

The angle between the vectors is calculated as follows;

θ = arc tan (y/x)

θ = arc tan (0/2)

θ = arc tan (0)

θ = 0⁰

The angle between the two vectors is 0⁰, thus the two vectors are parallel to each other.

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Answer: C. 90°

Explanation:

Answer:

1 m = 39.37 in = 3.281 ft

1500 m * 3.281 ft / m = 4922 ft

(5280 - 4922) / 4922 = .073 = 7.3 %

(Note - 1600 m often replaces the 1 mi run)

Gravity follows an inverse square law. This means that if the distance between two masses is decreased by a factor of 4, the gravitational force between those two masses: C. increases by a factor of 16.

Gravitational force is an attractive force that exists between all objects with mass; an object with mass attracts another object with mass; the magnitude of the force is directly proportional to the masses of the two objects and inversely proportional to the square of the distance between the two objects.

Force between two masses = G M1 M1 / [tex]R^{2}[/tex]

since , gravitation force d follows an inverse square law

F is directly proportional to 1/[tex]R^{2}[/tex]

If distance between two masses is decreased by a factor of 4

Let initial distance  : R

when distance between two masses is decreased by a factor of 4 = 4R

Force  = G M1 M1 / [tex](4R)^{2}[/tex]

Force =  G M1 M1 / [tex]16R^{2}[/tex]

16 Force = G M1 M1 / [tex]R^{2}[/tex]

since , there is an inverse relation , so if distance is decreased , gravitation force will increase .

hence, gravitational force will increase by factor of 16

correct option C. increases by a factor of 16.

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The  energy of photon in kJ/mol is 329kJ/mol.

Wavelength of radiation is 370nm. The frequency of given wavelength is

            ν = c / λ

            ν = 3×10^8 / 370×10^-9

            ν = 8.11 × 10^14 s^-1

      Now the energy of photon is:

             E = hν

             E = 6.63×10^-34  J.s/photon × 8.11×10^14s^-1

             E = 5.41× 10^-19  J/photon

         To find in mole

              E = 5.41× 10^-19 × 6.022×10^23

               E = 3.29 ×10^ 5 J/mol

   So, the energy of mole of photon is equal to 329 kJ/mol.

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True. The partial pressure of gas that is made up of a mixture of gases is the sum of the individual pressure of the gases.

Dalton's law of partial pressure of gases is one of the gas laws that take into consideration the fact that a gas can be made from a mixture of non-reacting gases.

According to him, if a gas is made as such, the pressure of the gas would be the sum of the individual pressure of the component gases. This means that each gas contributes partially to the overall pressure of the gas mixture.

Thus, if gas A is a mixture of gas B and gas C. The pressure, P, of gas A is given as:

P = Pb + Pc where Pb and Pc are the partial pressure of gases B and C respectively.

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The volume of any rectangular solid, including a cube, is calculated mathematically as V = l × w × h

In a given calculation, if you are given the:

To find this, you would have to use the area of its base which is:

Length * Width * Height.

Furthermore, if the cross-section is parallel, then you would have to solve it thus:

Length * Width which is the area of the section from top to bottom.

Although your question is incomplete, the general idea of how to find the cross-sectional area of the volume of any rectangular solid.

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Years of research have demonstrated that rats are intelligent creatures who experience pain and pleasure, care about one another, are able to read the emotions of others, and would assist other rats, even at their own expense.

In trials carried out at Brown University in the 1950s, rats were trained to press a lever for food, but they stopped pressing the lever when they noticed that with each press, a rat in an adjacent cage would scream in pain (after experiencing an electric shock).

Rats were trained to press a lever to lower a block that was hanging from a hoist by electric shocks administered by experimenters. A rat was subsequently hoisted into a harness by the experimenters, and according to their notes, "This animal normally shrieked and wriggled sufficiently while dangling, and if it did not, it was jabbed with a sharp pencil until it exhibited indications of discomfort." Even if it wasn't in danger of receiving a shock, a rat watching the scenario from the floor would pull a lever to lower the hapless rodent to safety.

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The image formed will be located between the focal point, f and double of the distance from focal point, 2f.

A convex lens is the name given to any converging lens.

A converging lens or convex lens is a lens that converges rays of light that are traveling parallel to its principal axis.

The focal length, f of a lens is  the distance between the center of a lens  and its focus.

For an object that is placed between infinity and double of the distance from focal point, along a line perpendicular to the center of the lens,

The image formed will be located between the focal point, f and double of the distance from focal point, 2f.

Thus, for an object placed between infinity and 2f from the lens along a line perpendicular to the center of the lens. The image formed will be located between the focal point, f and double of the distance from focal point, 2f.

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Answer: A 100-lb child stands on a scale while riding in an elevator. Then, the scale reading approaches to 100lb, while the elevator slows to stop at the lowest floor

Explanation: To find the correct answer, we need to know more about the apparent weight of a body in a lift.

                             [tex]ma=mg-N\\N=mg-ma[/tex]    i.e. during riding the scale reads a weight less than that of actual weight.

Thus, from the above explanation, it is clear that ,when the elevator moves to the lowest floor slowly and stops, then the apparent weight will become the actual weight.

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Magnetic field lines point leave north poles and enter south poles.

This is referred to as the direction that a small compass points when placed at a location.

They are closed curves which runs from the north pole and enters the south pole thereby making it the most appropriate choice.

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Pelvic girdle

In human anatomy, the pelvis is a complex of bones that connects the trunk and the legs, supports and balances the trunk, and houses and supports the intestines, the urinary bladder, and the internal organ. It is sometimes referred to as the bony pelvis or the pelvic girdle.
One is located on the left side of the body and the other is located on the right. They come together to make the pelvic girdle, a portion of the pelvis. The hip bones are attached to the upper portion of the skeleton at the sacrum.
The pelvic girdle's main function is to support the upper body's weight while seated and transfer that weight to the lower limbs while standing. For the muscles in the trunk and lower limbs, it functions as attachment point.

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1MeV = 1.6 x 10-13 J and  3.5 x 1011 joules of energy is energy in joules per kilogram of reactants.

The amount of fuel needed to meet US expectations for energy consumption over the next ten years.
In the US, each person uses 3.5 x 1011 joules of energy annually. 310,000,000 people make up the present population, thus use 1MeV = 1.6 x 10-13 J in your calculations.
In the US, annual energy consumption per person is equal to 3.5 x 1011Joules (estimated, varies by source, August 2009)
USA population: 310,000,000, roughly.
One mega electron volt, or one million electron volts, is designated as MeV. A particle with one electron charge will gain one MeV of energy when it passes through a potential difference of one million volts in a vacuum.

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The optic chiasm is the point where the optic nerves cross the midline, allowing the opposite side of the brain to process sensory data from one side of the body.

Since the optic nerves cross in the optic chiasm, also known as the optic chiasma, it plays a crucial role in the visual pathway. Within the suprasellar cistern, it is situated 10 mm above the pituitary gland and 10 mm beneath the hypothalamus near the base of the brain.

The optic chiasm's function is to make sure that visual impulses reach both hemispheres of the brain. The thalamus receives and processes the majority of brain impulses, which are then transmitted to various parts of the occipital lobe. Half of each divided optic nerve's fibers travel to the opposing side. Due to the anatomical configuration, injury to the optic nerve system results in particular patterns of vision loss.

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400 J power will be delivered by lifting a stone of mass 2 kg at the height of 20m in two minutes.

The quantity of energy transferred or transformed per unit of time is known as power. The watt, or one joule per second, is the unit of power in the International System of Units. Power is also referred to as an activity in ancient writings. A scalar quantity is a power.

Work completed and time is linked in the power equation. Since forces may move objects and we know that forces perform work, we might anticipate that by understanding the power, we can gain insight into how a body moves through time. This outcome may be especially beneficial.

Given that, a stone ‘X’ of mass 2 kg is lifted to the height of 20m in two minutes, and g=10 m/s-2

Power Delivered = Work done in lifting the stone

Work Done = Potential energy = mgh

Work done = 2 × 10 × 20

Work done = 400 J

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The angle of projection is θ = 53°

R = 3H

R = v²sin2θ/g   = 2v²sinθcosθ/2 = 3v²sin²θ/2g

    tan θ = 4/3

     θ = 53°

So,  the angle of projection is   θ = 53°

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Vega, the brightest star in the constellation lyra, has a parallax angle of approximately 0.13 arcseconds,  approximately  Vega will be 25.076 Light year or 7.692 Parsec away from the sun

The parallax angle is the angle between the Earth at one time of year, and the Earth six months later, as measured from a nearby star.

Mathematically it can be understood as that the parallax angle is the angle which is taken from a point at one time on the earth and again after six months later from the same point on the earth. The parallax angle is the semi-angle of inclination between the two lines to sight.

Stellar parallax is the basis for the parsec, which is the distance from the Sun to an astronomical object that has a parallax angle of one arcsecond.

Distance (in parsec) = 1 / (parallax angle ( arcsec))

given

parallax angle = 0.13 arcseconds

Distance (in parsec) = 1/ 0.13 = 7.692 Parsec

if 1 Parsec = 3.26 Light year

So, 7.692 Parsec will be equal to =  3.26 * 7.692 = 25.076 Light year

                                                        ≈ 25.076 Light year

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The net electric field at point D is determined as 3.95 x 10⁷ N/C.

E = kq/r²

where;

E(AD) = (9 x 10⁹ x 6 x 10⁻⁶)/(0.05²)

E(AD) = 2.16 x 10⁷ i N/C

E = kq/r²

where;

r² = 5²  + 5²

r² = 50

r = √50

r = 7.07 cm

E(BD) = (9 x 10⁹ x 5 x 10⁻⁶)/(0.0707²)

E(BD) = 9 x 10⁶ N/C

in x - direction = 9 x 10⁶ N/C x cos(45) = 6.36 x 10⁶ i  N/C

in y - direction = 9 x 10⁶ N/C x sin(45) = 6.36 x 10⁶j  N/C

E = kq/r²

where;

E(CD) = (9 x 10⁹ x 6 x 10⁻⁶)/(0.05²)

E(CD) = 2.16 x 10⁷ j N/C

Ei = 2.16 x 10⁷ i N/C  + 6.36 x 10⁶ i  N/C

Ei = 2.796 x 10⁷ i N/C

Ej = 2.16 x 10⁷ j N/C  + 6.36 x 10⁶j  N/C

Ej = 2.796 x 10⁷ j N/C

E = √Ei² + Ej²

E = √[(2.796 x 10⁷)² + (2.796 x 10⁷)²]

E = 3.95 x 10⁷ N/C

Thus, the net electric field at point D is determined as 3.95 x 10⁷ N/C.

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What is Law of conservation of charge?

Law of conservation of charge states that, "the total electric charge in an isolated system is always constant".

It can also be stated as, "Charge can neither be created nor destroyed but can only be converted from one form of energy to another".

What are the properties of conductors?

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Answer:

f=110HZ

Explanation:

Calculate the frequency of a wave

Based on equation λ= VT but T= 1/f

=> λ=V/f

=> f= V/λ

by V=22m/s

λ= 0.20m

=> f= 22/0.20= 22/(2×10-¹) = 110Hz

So the frequency of a wave is f=110Hz

Answer:

110

Explanation:

velocity=wavelength×frequency

22=0.20f

divide both sides by 0.20

22/0.20=0.20f/0.20

f=22/0.20

f=110

No, the light emitted from the source is not polarized

Bypassing it through a polarizing filter or other polarizing substance, light can be made polarized. After passing through a polarizing filter, the intensity of polarized light I is equal to the original intensity I0 cos2, where I0 is the original intensity and is the angle formed by the polarization's direction and the filter's axis.

Unpolarized light is diminished by a factor of 12 when it travels through a polarizer. Along the polarizer's axis, the transmitted light is polarized. The only parameter that is unaffected by any phenomenon, including reflection, refraction, interference polarization, etc., is frequency. The polarization phenomenon has no effect on light frequency.

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A long narrow solenoid has length l and a total of N turns, each of which has cross-sectional area A. Its inductance is μ₀ ( [tex]\frac{N^2A}{l}[/tex] ).

To find the answer, we need to know about the magnetic field due to a solenoid.

                             [tex]B=[/tex] μ₀n [tex]I[/tex]

                               [tex]n=\frac{N}{l}[/tex]

                            Φ [tex]= BA[/tex] Where, A is the area.

                                       Ф [tex]= \frac{NIA}{l}[/tex] μ₀

                                        Ф [tex]= LI[/tex]

                                        μ₀ ( [tex]\frac{N^2A}{l}[/tex] ) [tex]I[/tex]  [tex]=LI[/tex]

                                         [tex]L=[/tex] μ₀ ( [tex]\frac{N^2A}{l}[/tex] ).

Thus, we can conclude that the expression for inductance is  μ₀ ( [tex]\frac{N^2A}{l}[/tex] ).

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The inductance of a solenoid having N number of turns, area A and a length l will be equal to μ₀ ( [tex]\frac{N^2A}{l}[/tex]).

We need to understand the magnetic field created by a solenoid in order to determine the solution.

                                    [tex]B=\frac{NI}{l}[/tex]×μ₀

                                   [tex]flux=BA[/tex]  , A is the area.

                                      [tex]flux=\frac{NIA}{l}[/tex] times the μ₀.

                                        [tex]flux=IL[/tex]

                                     μ₀ ( [tex]\frac{N^2AI}{l}[/tex])= [tex]LI[/tex]

                                     [tex]L=[/tex] μ₀ ( [tex]\frac{N^2A}{l}[/tex]).

As a result, we can say that the inductance expression is   [tex]L=[/tex] μ₀ ( [tex]\frac{N^2A}{l}[/tex]).

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The value of each resistor is 23.51 ohms.

The value of each resistor is calculated as follows;

R₁ = R₂ = R₃ = R

Total resistance, Rt = 3R

V = IRt

V = I(3R)

R = V/3I

R = (67)/(3 x 0.95)

R = 23.51 ohms

Thus, the value of each resistor is 23.51 ohms.

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frequency fapproach is heard by a passenger = 302.05 Hz

frequency frecede is heard by a passenger = 228.37433 Hz

Given :

speed of train to the ground = 30.0 m/s

frequency emitted by the train whistle = 262 Hz

speed of sound in air = 344 m/s

To Find :

(A) frequency fapproach (B) frequency frecede

Solution :

The frequency of approach is given by

f' = f v + v(relative)

v - v(air)

= 262x 344 + 18

344 - 30

f' = 302.05 Hz

The frequency of approach is 302.05 Hz

The frequency of recede is given by

f' = f v - v(relative)

v + v(air)

= 262 x 344 - 18

344 + 30

The frequency of recede is 228.37433 Hz

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Answer:

Approximately [tex]13\; {\rm N \cdot m^{-1}}[/tex] (assuming that [tex]g = 9.81\; {\rm N \cdot kg^{-1}}[/tex].)

Explanation:

Let [tex]F_{\text{s}}[/tex] denote the force that this spring exerts on the object. Let [tex]x[/tex] denote the displacement of this spring from the equilibrium position.

By Hooke's Law, the spring constant [tex]k[/tex] of this spring would ensure that [tex]F_\text{s} = -k\, x[/tex].

Note that the mass of the object attached to this spring is [tex]m = 540\; {\rm g} = 0.540\; {\rm kg}[/tex]. Thus, the weight of this object would be [tex]m\, g = 0.540\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \approx 5.230\; {\rm N}[/tex].

Assuming that this object is not moving, the spring would need to exert an upward force of the same magnitude on the object. Thus, [tex]F_{\text{s}} = 5.230\; {\rm N}[/tex].

The spring in this question was stretched downward from its equilibrium by:

[tex]\begin{aligned} x &= (70\; {\rm cm} - 110\; {\rm cm}) \\ &= (-40)\; {\rm cm} \\ &= (-0.40) \; {\rm m}\end{aligned}[/tex].

(Note that [tex]x[/tex] is negative since this displacement points downwards.)

Rearrange Hooke's Law to find [tex]k[/tex] in terms of [tex]F_{\text{s}}[/tex] and [tex]x[/tex]:

[tex]\begin{aligned} k &= \frac{F_{\text{s}}}{-x} \\ &\approx \frac{5.230\; {\rm N}}{-(-0.40)\; {\rm m}} \\ &\approx 13\; {\rm N \cdot m^{-1}}\end{aligned}[/tex].