Which scientist proposed a mathematical solution for the wave nature of light?

Answer:

221 lines per millimetre

Explanation:

We know that for a diffraction grating, dsinθ =mλ where d = spacing between grating, θ = angle to maximum, m = order of maximum and λ = wavelength of light.

Since the grating is 42.0 cm from the screen and its first order maximum (m = 1) is at 6.09 cm from the center of the pattern,

tanθ = 6.09 cm/42.0 cm = 0.145

From trig ratios, cot²θ + 1 = cosec²θ

cosecθ = √((1/tanθ)² + 1) = √((1/0.145)² + 1) = √48.562 = 6.969

sinθ = 1/cosecθ = 1/6.969 = 0.1435

Also, sinθ = mλ/d at the first-order maximum, m = 1. So

sinθ = (1)λ/d = λ/d

Equating both expressions we have  

0.1435 = λ/d

d = λ/0.1435

Now, λ = 650 nm = 650 × 10⁻⁹ m

d = 650 × 10⁻⁹ m/0.1435

d = 4529.62 × 10⁻⁹ m per line

d = 4.52962 × 10⁻⁶ m per line

d = 0.00452962 × 10⁻³ m per line

d = 0.00452962 mm per line

Since d = width of grating/number of lines of grating

Then number of lines per millimetre = 1/grating spacing

= 1/0.00452962

= 220.77 lines per millimetre

≅ 221 lines per millimetre since we can only have a whole number of lines.

Answer:

e. the point about which the torque is to be calculated

Explanation:

torque is the product of a force and a distance

the point about which the torque is calculated is required to know the distance.

None of the other terms are relevant as they refer to mass or its equivalent, and velocity. Force is not mentioned in any of them.

A particle moves along the x-axis. In order to calculate the torque on the particle, you need to know the point about which the torque is to be calculated. Therefore, option E is correct.

The rotating equivalent of force is torque. Depending on the subject of study, it is also known as the moment, moment of force, rotating force, or turning effect. It illustrates how a force can cause a change in the body's rotational motion.

Ancient Romans gave these necklaces the term "torque" by describing them as twisted and spiral screw-shaped using the Latin word "torquere," which also means "twisting" and "turning."

It's critical to realize that torque, which has to do with your motor's power in terms of rotational force, is not the same thing as speed. Find a motor with a top speed if you require more motor speed, and a motor with a motor torque that is maximized if you need more rotational force.

Thus, option E is correct.

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Answer:

red blood cell, also called erythrocyte

Explanation:

Hope it helps

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Answer:

8.65x10^3m

Explanation:

See attached file

Answer:

check photo for solve

Explanation:

Answer:

The mas unit is the the 'Kilogram' written as 'kg'

Volume is 10 L

Explanation:

The complete question is

If you have a density of 100 kg/L, and a mass of 1000 units, tell me the following: First, what are the mass units?

Second, what is the volume

mass units is the 'Kilogram', written as 'kg'

density = mass/volume = 100 kg/L

the mass  = 1000 kg

volume = mass/density = 1000/100 = 10 L

Answer:

T = 3.14 hours

Explanation:

We need to find the orbital period (in hours) of an observation satellite in a circular orbit 1,787 km above Mars.

We know that the radius of Mars is 3,389.5 km.

So, r = 1,787 + 3,389.5 = 5176.5 km

Using Kepler's law,

[tex]T^2=\dfrac{4\pi ^2}{GM}r^3[/tex]

M is mass of Mars, [tex]M=6.39\times 10^{23}\ kg[/tex]

So,

[tex]T^2=\dfrac{4\pi ^2}{6.67\times 10^{-11}\times 6.39\times 10^{23}}\times (5176.5 \times 10^3)^3\\\\T=\sqrt{\dfrac{4\pi^{2}}{6.67\times10^{-11}\times6.39\times10^{23}}\times(5176.5\times10^{3})^{3}}\\\\T=11334.98\ s[/tex]

or

T = 3.14 hours

So, the orbital period is 3.14 hours

Answer:

The distance is [tex]d = 193.6 \ m[/tex]

Explanation:

From the question we are told that

   The time interval between the sounds is  k[tex]t_1 = k + t_2[/tex] =  0.50 s

    The  speed of sound in air is  [tex]v_s = 343 \ m/s[/tex]

    The  speed of sound in the concrete is [tex]v_c = 3000 \ m/s[/tex]

Generally the distance where the collision occurred is  mathematically represented as

          [tex]d = v * t[/tex]

Now from the question we see that d is the same for both sound waves

 So

        [tex]v_c t = v_s * t_1[/tex]

Now  

So [tex]t_1 = k + t[/tex]

      [tex]v_c t = v_s * (t+ k)[/tex]

=>     [tex]3000 t = 343* (t+ 0.50)[/tex]

=>    [tex]3000 t = 343* (t+ 0.50)[/tex]

=>    [tex]t = 0.0645 \ s[/tex]

So

     [tex]d = 3000 * 0.0645[/tex]

     [tex]d = 193.6 \ m[/tex]

Answer

1.07E22 Joules

Explanation;

We know that mass expands by a factor

=>>1/√[1-(v/c)²]

But v= 0.509c

So

1/√(1 - 0.509²)

=>>> 1/√(1 - 0.2591)

= >> 1/√(0.7409) = 1.16

But given that 121 tons is rest mass so 121- 1.16= 119.84 tons is kinetic energy

And we know that rest mass-energy equivalence is 9 x 10^19 joules per ton.

So Multiplying by 119.84

Kinetic energy will be 1.07x 10^22 joules

Answer:

m = 9.1 x 10⁶ kg

Explanation:

First, we need to find the rate of heat transfer through the box to the ice. For this purpose, we use Fourier's Law of Heat Conduction:

Q = KA ΔT/L

where,

Q = Rate Of Heat Transfer = ?

K = Thermal Conductivity = 0.16 KW/m.°C = 160 W/m.°C

A = Area = 1.5 m²

ΔT = Difference in Temperature = 29°C - 0°C = 29°C

L = Thickness of wall = 2 cm = 0.002 m

Therefore,

Q = (160 W/m °C)(1.5 m²)(29°C)/(0.002 m)

Q = 3.48 x 10⁶ W

Now, we find the amount of heat transferred in one day to the ice:

q = Qt

where,

q = amount of heat = ?

t = time = (1 day)(24 h/1 day)(3600 s/1 h) = 86400 s

Therefore,

q = (3.48 x 10⁶ W)(8.64 x 10⁴ s)

q = 3 x 10¹¹ J

Now, for mass of ice melted in a day:

q = m H

m = q/H

where,

m = mass of ice melted in a day = ?

H = latent heat of fusion of ice = 3.3 x 10⁵ J/kg

Therefore,

m = (3 x 10¹¹ J)/(3.3 x 10⁵ J/kg)

m = 9.1 x 10⁶ kg

Answer:

If the older generation is lacking, the younger generation would likely have knowledge, skill, or a positive attitude in some combination, but it is relative to the culture.

The simple reason is the desirability for genetic variation using recessive genes.

In other words, if the older generation lacks something, it tends to be something they don’t need, but something that will look good on young people. But mostly relative to the culture and education system.

Hope this helps

Answer:

They both have the same acceleration

Answer:

[tex]B=2.74\times 10^{-10}\ T[/tex]

Explanation:

It is given that,

A planar electromagnetic wave is propagating in the +x direction.The electric field at a certain point is, E = 0.082 V/m

We need to find the magnetic vector of the wave at the point P at that instant.

The relation between electric field and magnetic field is given by :

[tex]c=\dfrac{E}{B}[/tex]

c is speed of light

B is magnetic field

[tex]B=\dfrac{E}{c}\\\\B=\dfrac{0.082}{3\times 10^8}\\\\B=2.74\times 10^{-10}\ T[/tex]

So, the magnetic vector at point P at that instant is [tex]2.74\times 10^{-10}\ T[/tex].

The magnetic vector of the wave at the point P at that instant is [tex]2.73 \times 10^{-10}T[/tex]

The formula relating electric field and the magnetic field is given as;

[tex]c=\frac{E}{B}[/tex]

From the formula shown:

[tex]B=\frac{E}{c}\\B=\frac{0.082}{3.0\times 10^8}\\B=2.73 \times 10 ^{-10}T[/tex]

Hence the magnetic vector of the wave at the point P at that instant is [tex]2.73 \times 10^{-10}T[/tex]

Learn more on magnetic field here: https://brainly.com/question/21040756

Answer:

space exploration pays off in goods, technology, and paychecks. The work is done by people who are paid to do it here on Earth. The money they receive helps them buy food, get homes, cars, and clothing. They pay taxes in their communities, which helps keep schools going, roads paved, and other services that benefit a town or city. The money may be spent to send things "up there", but it gets spent "down here." It spreads out into the economy.

Answer:

About 23 meters

Explanation:

To do this, you'll want to apply one of the kinematic equations to find the time it takes for the cabin to reach max velocity from rest. (Use the max velocity as V_f and V_i=0)

Then, you can find the distance travelled during the acceleration by equating the acceleration to the change in distance of the time squared.

My work is in the attachment, comment if you have any questions.

Answer:

433

Explanation:

Answer:

The additional load is 20g

Answer:

There is no induced current on the coil.

Explanation:

Current is induced in a coil or a circuit, when there is a break of flux linkage. A break in flux linkage is caused by a changing magnetic field, and must be achieved by a relative motion between the coil and the magnet. Holding the magnet above the center of the coil will cause no changing magnetic filed since there is no relative motion between the coil and the magnet.

The height below the tower at which coin 1 pass coin 2 is 89.04 m.

The given parameters:

height of the tower, h = 100 m

initial velocity of coin 1, v = 15 m/s

time spent in air by coin 1 before coin 2 was dropped = 2s

To find:

Find the maximum height attained by coin 1 before falling to the ground:

[tex]v^2 = u^2 - 2gh\\\\where;\\\\v \ is \ the \ final \ velocity \ of \ coin \ 1 \ at \ maximum \ height, v \ = 0\\\\0 = (15^2) - 2(10)h\\\\20h = 225\\\\h = \frac{225}{20} \\\\h = 11.25 \ m[/tex]

Find the time taken for coin 1 to fall to the ground:

Total height of coin 1 above the ground, H = 11.25 m + 100 m = 111.25 m

[tex]t = \sqrt{\frac{2H}{g} } \\\\t = \sqrt{\frac{2\times 111.25}{10} } \\\\t = 4.72 \ s[/tex]

But the time taken for the coin 1 to reach 11.25 m above the tower:

[tex]t_1 = \sqrt{\frac{2h}{g} } \\\\t_1 = \sqrt{\frac{2\times 11.25}{10} } \\\\t_1 = 1.5 \ s[/tex]

Total time spent by coin 1 before reaching ground with respect to coin 2:

time = (1.5 s + 4.72 s) - 2 s

time = 4.22 s

Note: the 2 s was subtracted to keep both coins at a fair starting time below the tower.

Find the total time taken for coin 2 to fall to the ground:

Height of coin 2 above the ground = 100 m

Total time taken by coin 2 before falling to the ground is calculated as:

[tex]t_2 = \sqrt{\frac{2(100)}{10} } \\\\t_2 = 4.47s[/tex]

The time  at which coin 1 will pass coin 2 is 4.22 s.

Find the height below the tower when the time is 4.22 s.

[tex]h = \frac{1}{2} (10)(4.22)^2\\\\h = 89.04 \ m[/tex]

Thus, the height below the tower at which coin 1 pass coin 2 is 89.04 m.

Learn more here: https://brainly.com/question/18943273

Answer and Explanation:

The computation of the shortest wavelength in the series is shown below:-

[tex]\frac{1}{\lambda} = R(\frac{1}{n_f^2} - \frac{1}{n_i^2} )[/tex]

Where

[tex]\lambda[/tex] represents wavelength

R represents Rydberg's constant

[tex]n_f[/tex] represents Final energy states

and [tex]n_i[/tex] represents initial energy states

Now Substitute is

[tex]1.097\times 10^7\ m^{-1}\ for\ R, \infty for\ n_i,\ 3 for\ n_i,\\\\\ \frac{1}{\lambda} = R(\frac{1}{n_f^2} - \frac{1}{n_i^2} )[/tex]

now we will put the values into the above formula

[tex]= 1.097\times 10^7 m^{-1}(\frac{1}{3^2} - \frac{1}{\infty^2} )\\\\ = 1.097\times10^7\ m^{-1} (\frac{1}{9} )[/tex]

[tex]= 1218888.889 m^{-1}[/tex]

Now we will rewrite the answer in the term of [tex]\lambda[/tex]

[tex]\lambda = \frac{1}{1218888.889} m\\\\ = 0.82\times 10^{-6} m[/tex]

So, the whole Paschen series is in the part of the spectrum.

Answer:

1.36 m/s

Explanation:

I = ½mR²

τ = FR

α = τ/I = FR / (½mR²) = 2F/mR

a = Rα = 2F/m

s = θR

v² = u² + 2as

u = 0

v = √2as = √(2(2F/m)(θR)) = 2√(FθR/m)

v = 2√(29.0(0.400)(2π)(0.280) / 43.9) = 1.3636272...

Answer:

θ = 45.15°

Explanation:

We need to use the grating equation in this question. The grating equation is given as follows:

mλ = d Sin θ

where,

m = order number = 3

λ = wavelength of light = 520 nm = 5.2 x 10⁻⁷ m

d = slit spacing = 2.2 μm = 2.2 x 10⁻⁶ m

θ = angle from the axis = ?

Therefore,

(3)(5.2 x 10⁻⁷ m) = (2.2 x 10⁻⁶ m) Sin θ

Sin θ = (3)(5.2 x 10⁻⁷ m)/(2.2 x 10⁻⁶ m)

Sin θ = 0.709

θ = Sin⁻¹(0.709)

θ = 45.15°

Answer:

3.30 x 10^-7 Pascal

Explanation:

distance r = 1.5 m

power P = 700 W

the radiation pressure is given as

Pr = P/A*c

where

area of the surface A = 4πr^2

calculate for A

speed of light is c = 3×10^8  m/s

plugging above values in equation above gives

Pr = 3.30 x 10^-7 Pascal

Answer:

3.5 m/s

Explanation:

There are 3 forces on the cyclist:

Weight force mg pulling down,

Normal force N pushing up,

and friction force Nμ pushing left.

Sum of forces in the y direction:

∑F = ma

N − mg = 0

N = mg

∑F = ma

-Nμ = ma

-mgμ = ma

a = -gμ

a = -(10 m/s²)(0.60)

a = -6 m/s²

Velocity reached at end of 11 m:

v² = v₀² + 2aΔx

v² = (12 m/s)² + 2 (-6 m/s²) (11 m)

v = √12 m/s

v ≈ 3.5 m/s

Answer:

Alp decay.

Explanation:

From the above equation, the parent nucleus 185 79Au produces a daughter nuclei 181 77 Ir.

A careful observation of the atomic mass of the parent nucleus (185) and the atomic mass of the daughter nuclei (181) shows that the atomic mass of the daughter nuclei decreased by a factor of 4. Also, the atomic number of the daughter nuclei also decreased by a factor of 2 when compared with the parent nucleus as shown in the equation given above.

This simply means that the parent nucleus has undergone alpha decay which is represented with a helium atom as 4 2He.

Therefore, the equation is an example of alpha decay.

Answer:

statement 1 with answer C

statement 2 with answer F

statement 3 with answer B

Statement 1 with E

Statement 2 with A

Statement 3 with D

Explanation:

In this exercise you are asked to relate each with the answers

In general, in the optics diagram,

* Ray 1 is a horizontal ray that after stopping by the optical system goes to the focal point

* Ray 2 is a ray that passes through the intercept point between the optical axis and the system and does not deviate

* Ray 3 is a ray that passes through the focal length and after passing the optical system, it comes out horizontally.

With these statements, let's review the answers

statement 1 with answer C

statement 2 with answer F

statement 3 with answer B

Statement 1 with E

Statement 2 with A

Statement 3 with D

Answer:

Current, I = 1.23 A

Explanation:

Given that,

Inductance, L = 35 mH

Resistance, R = 12 ohms

Potential difference, V = 18 V

We need to find current 5 ms after the switch is closed. Current in LR circuit is given by :

[tex]I=I_o(1-e^{-t/\tau })[/tex] ....(1)

Here,

[tex]I_o[/tex] is final current

[tex]I_o=\dfrac{V}{R}\\\\I_o=\dfrac{18}{12}=1.5\ A[/tex]

[tex]\tau[/tex] is time constant

[tex]\tau=\dfrac{L}{R}\\\\\tau=\dfrac{35\times 10^{-3}}{12}\\\\\tau=0.00291\ s[/tex]

So, equation (1) becomes :

[tex]I=1.5\times (1-e^{-5\times 10^{-3}/0.00291})\\\\I=1.23\ A[/tex]

So, after 5 ms the current in the circuit is 1.23 A.

Answer:

Explanation:

The moment of inertia of the disk I  = 1/2 m R² where R is radius of the disc and m is its mass .

putting the values

I = .5 x 95 x .38²

= 6.86 kg m²

n = 87 rpm = 87 / 60 rps

n = 1.45 rps

angular velocity ω = 2π n , n is frequency of rotation .

= 2 x 3.14 x 1.45

= 9.106 radian /s

frictional force = 16 x .2

= 3.2 N

torque created by frictional force = 3.2 x .38

= 1.216 N.m

angular acceleration = torque / moment of inertia

= - 3.2 / 6.86

α  = - 0.4665 rad /s²

b ) ω² = ω₀² +  2 α θ , where α is angular acceleration

0 = 9.106² - 2 x .4665 θ

θ = 88.87 radian

no of turns = 88.87 / 2π

= 14.15  turns

Answer: μ = 0.8885

Explanation: Force due to friction is calculated as: [tex]F_{f} = \mu.N[/tex]

At an inclined plane, normal force (N) is: N = mgcosθ, in which θ=32.51.

Power associated with work done by friction is [tex]P=F_{f}.x[/tex]. The variable x is displacement the object "spent its energy".

Power associated with work done by gravitational force is P = mghcosθ, where h is height.

The decline forms with horizontal plane a triangle as draw in the picture.

To determine force due to friction:

[tex]F_{f}.x=mghcos(\theta)[/tex]

[tex]F_{f}=\frac{mghcos(\theta)}{x}[/tex]

Replacing force:

[tex]\frac{m.g.h.cos(\theta)}{x} = \mu.m.g.cos(\theta)[/tex]

[tex]\mu=\frac{h}{x}[/tex]

Calculating h using trigonometric relations:

[tex]sin(32.51) = \frac{h}{1}[/tex]

h = sin(32.51)

Coefficient of Kinetic friction is

[tex]\mu=\frac{sin(32.51)}{1}[/tex]

μ = 0.8885

For these conditions, coefficient of kinetic friction is μ = 0.8885.

Answer:

The point of contraflexure (PoC) occurs where bending is zero and at the point of change between positive and negative (or between compression and tension). In a beam that is flexing (or bending), the point where there is zero bending moment is called the point of contraflexure.