A single-slit diffraction pattern is formed on a distant screen. Assume the angles involved are small. Part A By what factor will the width of the central bright spot on the screen change if the wavelength is doubled

Answer:

Post indicator valve

Explanation:

Post Indicator Valves are commonly used to control the water flow of sprinkler systems used in public and private buildings, warehouses, and factories for fire suppression. PIVs control water flow from the public system into the building's fire suppression system.

Explanation:

1.The light reflected from the CD/DVD or soap bubble or oil film forms an interference with the surrounding light. The inference both constructive and destructive making some color appear and some disappear.

2.As light behaves as wave it will interfere differently at different angles. At certain angle it will interfere constructively and at certain angle it will interfere destructively making some color brighter and some disappear. So, at different angles the color are different.

Interference pattern is responsible for the formation of different colour when a light reflected from CD or soap bubble.

We can see colors when we look at reflected light from a CD or DVD disk, or a soap bubble or oil film on water because of the interference pattern. The colors that we see on the CD are created due to the reflection of white light from ridges in the metal. When light passes through something with many small ridges or scratches, we often see rainbow colors and interesting patterns.

These patterns are called interference patterns. White light is made up of 7 colors i.e. red, orange, yellow, green, blue, indigo, violet. The CD converts or separates the white light into 7 colors so we can conclude that interference pattern is responsible for the formation of different colour when a light reflected from CD OR soap bubble.

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Answer:

1. A

2. C

3. D

Explanation:

Answer:

96 m

Explanation:

Given:

v₀ = 0 m/s

a = 3 m/s²

t = 8 s

Find: Δx

Δx = v₀ t + ½ at²

Δx = (0 m/s) (8 s) + ½ (3 m/s²) (8 s)²

Δx = 96 m

Answer:

Explanation:

The force experienced by the moving electron in the magnetic field is expressed as F = qvBsinθ where;

q is the charge on the electron

v is the velocity of the electron

B is the magnetic field strength

θ is the angle that the velocity of the electron make with the magnetic field.

Given parameters

F =  1.40*10⁻¹⁶ N

q = 1.6*10⁻¹⁹C

v = 3.94*10³m/s

B = 1.23T

Required

Angle that the velocity of the electron make with the magnetic field

Substituting the given parameters into the formula:

1.40*10⁻¹⁶ =  1.6*10⁻¹⁹ * 3.94*10³ * 1.23 * sinθ

1.40*10⁻¹⁶ = 7.75392 * 10⁻¹⁹⁺³sinθ

1.40*10⁻¹⁶ = 7.75392 * 10⁻¹⁶sinθ

sinθ = 1.40*10⁻¹⁶/7.75392 * 10⁻¹⁶

sinθ = 1.40/7.75392

sinθ = 0.1806

θ = sin⁻¹0.1806

θ₁ = 10.4⁰

Since sinθ is positive in the 1st and 2nd quadrant, θ₂ = 180-θ₁

θ₂ = 180-10.4

θ₂ = 169.6⁰

Hence, the angle that the velocity of the electron make with the magnetic field are 10.4⁰ and 169.6⁰

Answer:

The pressure increase inside the automobile engine block is 1782.18 ATM

Explanation:

Given;

the change in volume of water, ΔV = 9%

the bulk modulus of ice, K = 2 x 10⁹ N/m²

Bulk modulus is given by;

[tex]K = -V\frac{dP}{dV}[/tex]

for pressure increase in the automobile engine block, when the water in there froze;

[tex]dP = K(\frac{dV}{V} )\\\\dP = K(\frac{0.09V}{V} )\\\\dP = 0.09K\\\\dP = 0.09 (2*10^9)\\\\dP = 1.8 *10^{8} \ N/m^2\\\\dP = 1782.18 \ ATM[/tex]

Therefore,  the pressure increase inside the automobile engine block is 1782.18 ATM

The pressure increase inside your automobile engine block will be 1782.18 atm. The force involved vertical to the surface of an object per unit area is pressure.

The force applied perpendicular to the surface of an item per unit area across which that force is spread is known as pressure.

It is denoted by P. The pressure relative to the ambient pressure is known as gauge pressure.

The given data in the problem is;

ΔV is the  change in volume of water = 9%

K is the bulk modulus of ice = 2 x 10⁹ N/m²

dP is the change in the presure=?

The bulk modulus is found as;

[tex]\rm K=-V \frac{dp}{dv} \\\\[/tex]

The change in the presure is obtained as;

[tex]\rm dP = K\frac{dV}{V} \\\\ \rm dP = K\frac{0.09V}{V} \\\\ \rm dP = 0.09 K \\\\ \rm dP = 0.09 \times 2 \times 10^9 \\\\ \rm dP = 1.8 \times 10^8 \\\\ \rm dP =1782.18 \ atm[/tex]

Hence the pressure increase inside your automobile engine block will be 1782.18 atm.

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Answer:

0.09 x10^-10m

Explanation:

Using wavelength=( 12.27 A)/√V

= 12.27 x 10^-10/ √1.6x10^2

= 0.09x10^-10m

Answer:

The current in the ammeter is zero.

(1) is correct option.

Explanation:

Given that,

The capacitor is charged.

We need find the current after closed switched

We know that,

When switch is closed then the capacitor behave as a short circuit, and the all current flows through it. the current is zero.

Then, the ammeter reads zero.

Hence, The current in the ammeter is zero.

(1) is correct option.

Answer:

The actual distance is  [tex]d_a = 0.3233\ m[/tex]

Explanation:

From the question we are told that

     The  distance of the can is d =  43 cm  =  0.43 m

Generally the actual distance is mathematically represented as

         [tex]d_a = [\frac{ n_a }{n_w} ]* d[/tex]

Where  [tex]n_a , n_w[/tex] are the refractive index of air and water and their value is  

         [tex]n_a = 1 , \ \ \ n_w = 1.33[/tex]

So

       [tex]d_a = [\frac{ 1 }{1.33} ]* 0.43[/tex]

       [tex]d_a = 0.3233\ m[/tex]

Answer:

) pulls the ladder in the direction opposite

Explanation:

This is in line with lenz law that states that the magnetic field induced in a conductor act to oppose the magnetic field that produced it

Answer:

Speed of the electron is 2.46 x 10^8 m/s

Explanation:

momentum of the electron before relativistic effect = [tex]M_{0} V[/tex]

where [tex]M_{0}[/tex] is the rest mass of the electron

V is the velocity of the electron.

under relativistic effect, the mass increases.

under relativistic effect, the new mass M will be

M = [tex]M_{0}/ \sqrt{1 - \beta ^{2} }[/tex]

where

[tex]\beta = V/c[/tex]

c  is the speed of light = 3 x 10^8 m/s

V is the speed with which the electron travels.

The new momentum will therefore be

==> [tex]M_{0}V/ \sqrt{1 - \beta ^{2} }[/tex]

It is stated that the relativistic momentum is 1.75 times the non-relativistic momentum. Equating, we have

1.75[tex]M_{0} V[/tex] = [tex]M_{0}V/ \sqrt{1 - \beta ^{2} }[/tex]

the equation reduces to

1.75 = [tex]1/ \sqrt{1 - \beta ^{2} }[/tex]

square both sides of the equation, we have

3.0625 = 1/[tex](1 - \beta ^{2} )[/tex]

3.0625 - 3.0625[tex]\beta ^{2}[/tex] = 1

2.0625 = 3.0625[tex]\beta ^{2}[/tex]

[tex]\beta ^{2}[/tex] = 0.67

β = 0.819

substitute for  [tex]\beta = V/c[/tex]

V/c = 0.819

V = c x 0.819

V = 3 x 10^8 x 0.819 = 2.46 x 10^8 m/s

Explanation:

Distance = speed × time

d = (340 m/s) (9.6 s)

d = 3264 m

Answer:

Answers a) and b) should be marked as correct.

Explanation:

Recall that the resonance in an LRC circuit occurs when the current through the circuit is at its maximum, and such takes place when the impedance  (Z) of the circuit reaches its maximum. This means that the impedance (see formula below) is at its minimum value:

[tex]Z=\sqrt{R^2+(\omega\,L-\frac{1}{\omega\,C})^2 }[/tex]

as per the impedance expression above, such happens when the term in parenthesis inside the root which contains the inductive reactance ([tex]\omega\,L[/tex]) and the capacitive reactance ([tex]1/\omega\,C[/tex]) have the same value.

Therefore, answers:

a) "The impedance of the circuit has its minimum value."

and

b) "The inductive reactance and the capacitive reactance are exactly equal to each other."

are correct answers.

(a) The impedance of the circuit has its minimum value.

(b) The inductive reactance and the capacitive reactance are exactly equal to each other

LRC series circuit consists of inductor, resistor and capacitor is series.

The impedance of the circuit is calculated as follows;

[tex]Z = \sqrt{R^2 + (X_C -X_L)^2}[/tex]

where;

The impedance of the circuit is minimum when the capacitive reactance is equal to the inductive reactance.

[tex]X_C = X_L \\\\Z = \sqrt{R^2 \ + (0)^2} \\\\Z = R[/tex]

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Answer:

60 km/hour.

Explanation:

We'll begin by calculating the total distance traveled by the car. This is illustrated below:

Total distance traveled = sum of distance between PQRST

Total distance = 10 + 5 + 10 + 5

Total distance = 30 km

Next, we shall convert 30 mins to hour. This can obtained as follow:

Recall:

60 mins = 1 hour

Therefore,

30 mins = 30/60 = 0.5 hour.

Finally, we shall determine the average speed of the car as follow:

Distance = 30 km

Time = 0.5 hour

Speed =?

Speed = distance /time

Speed = 30/0.5

Speed = 60 km/hour

Therefore, the speed of the car is 60 km/hour.

Complete Question

Two stationary positive point charges, charge 1 of magnitude 3.25 nC and charge 2 of magnitude 2.00 nC , are separated by a distance of 58.0 cm . An electron is released from rest at the point midway between the two charges, and it moves along the line connecting the two charges.

Required:

What is the speed of the electron when it is 10.0 cm from the +3.25-nC charge?

Answer:

The velocity is [tex]v = 80.82 \ m/s[/tex]

Explanation:

From  the question we are told that

   The magnitude of charge one is  [tex]q_1 = 3.25 nC = 3.25 *10^{-9} \ C[/tex]

   The  magnitude of charge two  [tex]q_2 = 2.00 \ nC = 2.00 *10^{-9} \ C[/tex]

   The distance of separation is   [tex]d = 58.0 \ cm = 0.58 \ m[/tex]

Generally the electric potential of the electron at the midway point is mathematically represented as

         [tex]V = \frac{ q_1 }{\frac{d}{2} } + \frac{ q_2}{\frac{d}{2} }[/tex]

substituting values

         [tex]V = \frac{ 3.25 *10^{-9} }{\frac{ 0.58}{2} } + \frac{ 2 *10^{-9} }{\frac{ 0.58}{2} }[/tex]

          [tex]V = 1.8103 *10^{-8} \ V[/tex]

Now when the electron is 10 cm   =  0.10 m  from charge 1 , it is  (0.58 - 0.10 =  0.48 m ) m from charge two

Now the electric potential  at that point is mathematically represented as

       [tex]V_1 = \frac{q_1}{ 0.10} + \frac{q_2}{ 0.48}[/tex]

 substituting values

      [tex]V_1 = \frac{3.25 *10^{-9}}{ 0.10} + \frac{2.0*10^{-9}}{ 0.48}[/tex]

      [tex]V_1 = 3.67*10^{-8} \ V[/tex]

Now the law of energy conservation ,

   The  kinetic energy of the electron  =  potential energy of the electron

i.e     [tex]\frac{1}{2} * m * v^2 = [V_1 - V]* q[/tex]

where q is the magnitude of the charge on the electron with value

      [tex]q = 1.60 *10^{-19} \ C[/tex]

While m is the mass of the electron with value  [tex]m = 9.11*10^{-31} \ kg[/tex]

        [tex]\frac{1}{2} * 9.11 *10^{-19} * v^2 = [ (3.67 - 1.8103) *10^{-8}]* 1.60 *10^{-19}[/tex]

         [tex]v = \sqrt{6532.4}[/tex]

        [tex]v = 80.82 \ m/s[/tex]

Answer:

This means that mercury has a higher or faster expansion rate than glass

Explanation:

This is because When a container expands, the reservoir in the glass expands at the same rate as the glass. Thus, if there is something in a glass and both expand at the same rate, they have no change - but if the contents expand faster, they will fill the container to a higher level, and if the contents expand slower, they will fill the container to a lower level (relative to the new size of the container).

Answer:

d = 6.38 x 10⁻³ m = 6.38 mm

Explanation:

Since, the no. of bright fringes is 34 in a centimeter, therefore, the fringe spacing must be equal to:

Fringe Spacing = Δx = 1 cm/34

Δx = 0.0294 cm = 2.94 x 10⁻⁴ m

But, the formula for fringe spacing in a double slit experiment is:

Δx = λL/d

where,

λ = wavelength of light = 605 nm = 6.05 x 10⁻⁷ m

L = Distance between screen and slits = 3.1 m

d = slit separation = ?

Therefore,

2.94 x 10⁻⁴ m = (6.05 x 10⁻⁷ m)(3.1 m)/d

d = (18.755 x 10⁻⁷ m²)/(2.94 x 10⁻⁴ m)

d = 6.38 x 10⁻³ m = 6.38 mm

Answer:

Explanation:

Using the lens formula

1//f = 1/u+1/v

f is the focal length of the lens

u is the object distance

v is the image distance

For convex lens

The focal length of a convex lens is positive and the image distance can either be negative or positive.

Given f = 20cm and u = 10cm

1/v = 1/f - 1/u

1/v = 1/20-1/10

1/v = (1-2)/20

1/V = -1/20

v = -20/1

v = -20 cm

Since the image distance is negative, this shows that the nature of the image formed by the convex lens is a virtual image

For concave lens

The focal length of a concave lens is negative and the image distance is negative.

Given f = -20cm and u = 10cm

1/v = 1/f - 1/u

1/v = -1/20-1/10

1/v = (-1-2)/20

1/V = -3/20

v = -20/3

v = -6.67 cm

Since the image distance is negative, this shows that the nature of the image formed by the concave lens is a virtual image

Answer:

     λ = 52.5 nm

Explanation:

De Broglie's duality principle states that all matter has wave and particle characteristics, being related by the expression

          p = h / λ

where the moment

          p = mv

          λ = h / mv

let's calculate

        λ = 6.63 10⁻³⁴ / 1.675 10⁻²⁷ 7.54

        λ = 5.25 10⁻⁸ m

Let's reduce anm

       λ = 5.25 10⁻⁸ m (10⁹ nm / 1m)

       λ = 52.5 nm

Answer:

34°

Using the relation

θᶜ = sin^-1(n₂/n₁),

where n1= the refractive index of light is propagating from a medium

And n2 = refractive index of medium into which light is entering

So we know that

refractive index of diamond at 589nm = 2.41= n₁

refractive index of ethanol at 589nm and 20°C = 1.36= n₂

Thus. θᶜ = sin^-1(1.361/2.417) = 0.58radians = 34°

Explanation:

Answer:

The maximum force that can be lifted by this system is  51,478.4 kg

Explanation:

Given;

maximum gauge pressure of the hydraulic system, Hp = 15 atm = 1.52 x 10⁶ N/m²

diameter of the piston, d = 65 cm = 0.65 m

The maximum gauge pressure of the piston is given as;

[tex]Hp = \frac{F}{A}[/tex]

Where;

F is the maximum force of the piston

A is the area of the piston

[tex]A = \pi (\frac{0.65}{2} )^2\\\\A = 0.3319 \ m^2[/tex]

F = Hp x A

F = 1.52 x 10⁶N/m² x 0.3319m²

F = 504488 N

Force is given as;

F = mg

m = F/g

m = 504488/9.8

m = 51,478.4 kg

Therefore, the maximum force that can be lifted by this system is  51,478.4 kg

Answer:

4.5x 10^ -9m

Explanation:

See attached file

Answer:

The radius is  [tex]r_{min} = 0.00226 \ m[/tex]

Explanation:

   From the question we are told that

      The  elastic limit(stress) is [tex]\sigma = 5.0*10^{8} \ N /m^2[/tex]

      The length is  [tex]L = 4.0 \ m[/tex]

      The weight of the commercial sign is    [tex]F_s = 8000 \ N[/tex]

       The maximum extension of the wire is  [tex]\Delta L = 5.0 \ cm = 0.05 \ m[/tex]

Generally the elastic limit of an alloy (stress) is is mathematically represented as

            [tex]\sigma = \frac{ F_s }{ A }[/tex]

Where A is the cross-sectional area of the wire which is mathematically represented as

         [tex]A = \pi r^2[/tex]

here [tex]r = r_{min}[/tex] which is the minimum radius of the wire that support the commercial sign

So

          [tex]\sigma = \frac{ F_s }{ \pi r_{min}^2 }[/tex]

=>       [tex]r_{min} = \sqrt{\frac{F_s}{\sigma * \pi} }[/tex]

substituting values

             [tex]r_{min} = \sqrt{\frac{8000}{ 5.0* 10^8 * 3.142} }[/tex]

           [tex]r_{min} = 0.00226 \ m[/tex]

Answer:

Explanation:

Before calculating the work function, we must know the formula for calculating the kinetic energy of an electron. The kinetic energy of an electron is the taken as the difference between incident photon energy and work function of a metal.

Mathematically, KE =  hf - Ф where;

h is the Planck constant

f is the frequency = c/λ

c is the speed of light

λ is the wavelength

Ф is the work function

The formula will become KE =  hc/λ - Ф. Making the work function the subject of the formula we have;

Ф = hc/λ - KE

Ф = hc/λ - 1/2mv²

Given parameters

c = 3*10⁸m/s

λ = 97*10⁻⁹m

velocity of the electron v = 3.48*10⁵m/s

h = 6.62607015 × 10⁻³⁴

m is the mass of the electron = 9.10938356 × 10⁻³¹kg

Substituting the given parameters into the formula Ф = hc/λ - 1/2mv²

Ф =  6.63 × 10⁻³⁴*3*10⁸/97*10⁻⁹ -  1/2*9.11*10⁻³¹(3.48*10⁵)²

Ф = 0.205*10⁻¹⁷ - 4.555*10⁻³¹*12.1104*10¹⁰

Ф = 0.205*10⁻¹⁷ - 55.163*10⁻²¹

Ф = 0.205*10⁻¹⁷ - 0.0055.163*10⁻¹⁷

Ф = 0.1995*10⁻¹⁷Joules

Since 1eV = 1.60218*10⁻¹⁹J

x = 0.1995*10⁻¹⁷Joules

cross multiply

x = 0.1995*10⁻¹⁷/1.60218*10⁻¹⁹

x = 0.1245*10²

x = 12.45eV

Hence the work function of the metal in eV is 12.45eV

Answer:

the answer to your question us c honey

Answer:

C

Explanation:

This is so because different materials vary in resistance and conductance of current, heat. Metals are good conductors while none metals like rubber, plastic, glass etc are good insulators or resistors.

Answer:

The distance is [tex]y = 0.00162 \ m[/tex]

Explanation:

From the question we are told that

    The wavelength is  [tex]\lambda = 486 \ nm = 486 *10^{-9} \ m[/tex]

   The  slit spacing is  [tex]d = 0.600 \ mm = 0.60 *10^{-3} \ m[/tex]

    The distance of the screen is  [tex]D = 2.0 \ m[/tex]

 Generally the distance along the screen between adjacent bright fringes is mathematically represented as  

        [tex]y = \frac{\lambda * D}{d}[/tex]

substituting values

         [tex]y = \frac{ 486 *10^{-9} * 2}{0.6*10^{-3}}[/tex]

         [tex]y = 0.00162 \ m[/tex]

Answer:

145060km

Explanation: Given that

speed = dx/dt = 2t^2 +1

integrate

x = 2/3t^3 + t + c (c is constant, x is in km, t is in second)

given that at t=0, x = 1000

so 1000 = 2/3 X (0)^3 + 0 + c

or c = 1000

So x = 2/3t^3 + t + 1000

for t = 1 min = 60s

x = 2/3 X 60^3 + 60 + 1000

x = 2/3×216000+ 1060

x = 144000+1060

= 145060km

At one minute, it will be 145060km far from the earth

Answer:

6ms^-1

Explanation:

Given that the frequency difference is

( 563- 544) = 19

So alsoThe wavelength of each wave is = v/f = 344 /544

and there are 19 of this waves

So it is assumed that each motorcycle has moved 0.5 of this distance

in one second thus the speed of the motorcycles will be

=> 19/2 x 344/544 = 6.0 m/s

Answer:

it is either constant or zero

Explanation:

Answer:

a) Connect a series resistance of 8,47 ohms

b)14,16 [A]

c) r = 10,96 ohms

Explanation:

My blower requires 120 (v) then, I have to connect a series resistor to make the nominal 240 (v) of the European voltage outlet drop to 120 (V) but at the same time keep the level of current to operate my blower

In America

P = V*I

1700 (w) = 120*I

I = 1700/120 [A]

I = 14,16 [A]        current needed for the blower

In Europe

120 (v)  (the drop of voltage I need) when a current of 14,16 passes through to series  resistor is

V = I*R          120 = 14,16* R         R = 8,47 ohms

c) P = I*r²

1700 (w) = 14,16 (A) * r²

r² = 120,06

r = 10,96 ohms