The line of sight from a small boat to the light at the top of a 45-foot lighthouse built on a cliff 25 feet above the water makes a 20° angle with the water. To the nearest foot, how far is the boat from the cliff?

Answer:

(a). The eye's near point is 68.98 cm from the eye.

(b). The eye's far point is 33.33 cm from the eye.

Explanation:

Given that,

Power = 2.55 D

Object distance = 25 cm for near point

Object distance = ∞ for far point

Suppose where is the far point of an eye for which a contact lens with a power of -3.00 D  is prescribed for distant vision?

(a) We need to calculate the focal length

Using formula of power

[tex]f =\dfrac{1}{P}[/tex]

Put the value into the formula

[tex]f=\dfrac{100}{2.55}[/tex]

[tex]f=39.21\ cm[/tex]

We need to calculate the image distance

Using formula of lens

[tex]\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}[/tex]

Put the value into the formula

[tex]\dfrac{1}{39.21}=\dfrac{1}{v}-\dfrac{1}{-25}[/tex]

[tex]\dfrac{1}{39.21}-\dfrac{1}{25}=\dfrac{1}{v}[/tex]

[tex]\dfrac{1}{v}=-\dfrac{1421}{98025}[/tex]

[tex]v=-68.98\ cm[/tex]

The eye's near point is 68.98 cm from the eye.

(b). We need to calculate the focal length

Using formula of power

[tex]f =\dfrac{1}{P}[/tex]

Put the value into the formula

[tex]f=-\dfrac{100}{3.00}[/tex]

[tex]f=-33.33\ cm[/tex]

We need to calculate the image distance

Using formula of lens

[tex]\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}[/tex]

Put the value into the formula

[tex]\dfrac{1}{-33.33}=\dfrac{1}{v}-\dfrac{1}{\infty}[/tex]

[tex]-\dfrac{1}{33.33}+\dfrac{1}{\infty}=\dfrac{1}{v}[/tex]

[tex]\dfrac{1}{v}=-\dfrac{1}{33.33}[/tex]

[tex]v=-33.33\ cm[/tex]

The eye's far point is 33.33 cm from the eye.

Hence, (a). The eye's near point is 68.98 cm from the eye.

(b). The eye's far point is 33.33 cm from the eye.

The near point for which a lens of +2.55 diopters is prescribed is 71 cm.

We have to obtain the focal length of the lens as follows;

f = 100/P

Where P is the power of the lens in diopters.

f = 100/2.55 = 39.2 cm

Now;

Given that;

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

f = focal length

v = image distance

u = object distance

1/v = 1/u - 1/f

u = Near point of the normal  eye

1/v = 1/25 - 1/39.2

v = 71 cm

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Answer:

AB = 29

Explanation:

For a better understanding, we must work this problem in a graphic way. In the attached image we can see the solution.

First, we draw a vertical dotted lines from the point J & K to the line ML, then we can see two new portions with the same length. Then with this simple analysis:

2x = 39 - 19

x = 10

Then we know that x = 10, another important data to find the answer is that the AB line is located in the midpoints of the legs. We also can see the right triangle MJ and the dotted line.

Now for every single right triangle, no matter its size and relationship between the vertical and the horizontal lengths, if some point is located in the hypotenuse (leg) at the middle of its length. This will be proportional to the vertical and the horizontal cathetus, therefore we will have the middle point on those two lines.

So, the AB line will be the sum of JK plus two times 5

AB = 19 + 5 + 5 = 29

Answer:

d) the receiver should be moving at 300 m/s in the same direction as the jet.

Explanation:

The change in the frequency of a moving sound (or wave) source is called Doppler Effect. The change in frequency is:

[tex]\Delta f=\frac{\Delta v}{v}f_{o}[/tex] (1)

with [tex]\Delta v=\mid v_{r}-v_{s}\mid[/tex] the velocity of the receptor respect the source, [tex] f_{o} [/tex] the real frequency  and [tex] v [/tex] the velocity of the waves in the medium, we should be verty careful because the direction of the velocities are important so we have to select a reference frame and take on account the sign of the velocities. We're going to select positive direction as airplane direction. If we assume the frequency of the airplane sound and the velocity of waves on air remain constant, we should find the option that give us [tex] \Delta v=\mid v_{r}-v_{s}\mid = 300 [/tex] as the stationary case; let's see for:

a) [tex] \Delta v=\mid v_{r}-v_{s}\mid =\mid -900-600 \mid= 1500[/tex]

b) [tex]\Delta v=\mid v_{r}-v_{s}\mid = \mid-300-600 \mid= 900 [/tex]

c) [tex]\Delta v=\mid v_{r}-v_{s}\mid = \mid0-600\mid = 600 [/tex]

d) [tex]\Delta v=\mid v_{r}-v_{s}\mid= \mid300-600\mid = 300 [/tex]

So, the correct answer is d)

Answer:

We can cause delamination.

Explanation:

The reason why is because the probability of causing delamination increase considerably when we use Hole-filling fasteners. If we use a typical rivet, these tends to expands in order to fill the hole.

If we analyze the force applied by the expanded rod will cause that the matrial will be deteriorated and will cause that the material to delaminate around the edges of the hole and we can cause possible control and no protection to the material.

Answer:

1422.8 m

Explanation:

Given:

Displacement of the truck is, [tex]\vec S=1430\ m[/tex]

The direction of the truck's displacement is 5.76° with the horizontal.

A vector inclined at angle [tex]\theta[/tex] with the horizontal is resolved into 2 components which are mutually perpendicular to each other. One of the component is along the horizontal and the other is along the vertical.

If a vector 'A' is inclined at an angle [tex]\theta[/tex] with the horizontal, then its horizontal and vertical components are given as:

[tex]Horizontal:\\A_x=A\cos \theta\\\\Vertical:\\A_y=A\cos \theta[/tex]

Here, the vector is 'S' and its horizontal component is needed.

Therefore, the horizontal component is given as:

[tex]S_x=S\cos \theta\\S_x=1430\times \cos(5.76\°)\\S_x=1422.8\ m[/tex]

Answer:

19696 J or 19700 J

Explanation:

COMPONENT OF FORCE IN DIRECTION OF DISPLACEMENT IS

F cosФ = 200 cos 10° = 196.96 N

work = component of force in direction of displacement ×  displacement

        = 196.96 × 100

        = 19696 J

       = 19700 J

The work done by rope is equal to 19696 J on the skier during a forward displacement of 100 m

Work can be described as the energy used when a force is applied in order to move an object through a specific displacement. The performed work defines both the applied force and the displacement of the object.

The force acting is to move an object in a line in the direction of the pushing force over a distance 'd'.

W= F ×d

Where 'F' is the force and 'd' is the displacement and W is work done by an object.

If the angle θ  with the forward direction of motion then work = Fd cos θ

Given, the force acting, F = 200 N

The angle with the forward direction of motion, θ = 10°

Given, the displacement in the forward direction, d = 100 m

Work done by the rope, W = Fd cos θ

W = 200 × 100 cos 10°

W = 19696 J

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Answer:

w₁ =  40 rpm

Explanation:

Number of teeth of gear A = 10

Number of teeth of gear B =  40

Speed of gear B = w₂ = 10 rpm

Speed of gear A = w₁ = ?

Gear ratio is given by:

N₁/N₂ = w₂ / w₁

w₁ = N₂/N₁ * w₂

⇒ w₁ = 40/10 * 10

⇒ w₁ =  40 rpm

Gear A will turn at 40 rpms.

In this scenario, we can use the formula for calculating the speed of rotation of gears. The formula is based on the principle that the number of teeth on a gear is inversely proportional to its speed. In other words, the smaller the gear, the faster it rotates.

Using the formula, we can calculate the speed at which gear A turns:

Speed of gear A = (Number of teeth on gear B/Number of teeth on gear A) x Speed of gear B

Plugging in the values, we get:

Speed of gear A = (40/10) x 10 = 40 rpms

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Answer:

The mechanical energy of the helicopter is [tex]1.12\times 10^7\ J[/tex].

Explanation:

It is given that,

Mass of the helicopter, m = 3250 kg

Speed of the helicopter, v = 56.9 m/s

Position of the helicopter, h = 185 m

The energy possessed by an object due to its motion is called its kinetic energy. It is given by :

[tex]E=\dfrac{1}{2}mv^2[/tex]

[tex]E=\dfrac{1}{2}\times 3250\times (56.9)^2[/tex]  

[tex]E=5.26\times 10^6\ J[/tex]

The energy possessed by an object due to its position is called its potential energy. It is given by :

[tex]E=mgh[/tex]

[tex]E=3250\times 9.8\times 185[/tex]  

[tex]E=5.89\times 10^6\ J[/tex]

The sum of kinetic and potential energy is called mechanical energy of the system. It is given by :

[tex]M=5.26\times 10^6+5.89\times 10^6[/tex]

[tex]M=11.15\times 10^6\ J[/tex]

or

[tex]M=1.12\times 10^7\ J[/tex]

So, the mechanical energy of the helicopter is [tex]1.12\times 10^7\ J[/tex]. Hence, this is the required solution.

Answer:

36.87°

Explanation:

length of anchor (L) = 30 m

depth of water (d) = 18 m

find the angle of depression the anchor chain makes with the water level

from the diagram attached the anchor chain, the water bed and the depth of the water all form a right angle triangle

therefore

cos θ = [tex]\frac{d}{L}[/tex]

cos θ = [tex]\frac{18}{30}[/tex]

θ = [tex]cos^{-1}.\frac{18}{30}[/tex] = 53.13°

the angle of depression (Ф) = 90 - 53.13 = 36.87°

Answer:

b.The ultimate source of energy in the biosphere is the sun.

Explanation:

Answer: D.Large amounts of energy are lost in the transfer between trophic levels.

Explanation:

Final answer:

The gravitational power per meter length available in a wave of height 0.60 m is calculated using the gravitational potential energy per unit length formula, incorporating the known sea-water density, the wave height, and the acceleration due to gravity.

Explanation:

To estimate the gravitational power per meter length available in a wave of height 0.60 m with the given sea-water density of 1.2 × 103 kg/m3, we use the wave power equation derived from the concept of gravitational potential energy. The gravitational potential energy per unit length of the wave (E) is given by the formula E = ½ × ρgh2L, where ρ represents the density of the seawater, g is the acceleration due to gravity (which is approximately 9.81 m/s2), h is the wave height, and L is the length of the wave under consideration.

Substituting the values, with wave height (h) as 0.60 m and considering a unit length (L = 1 m) for power per meter, we get:

E = ½ × (1.2 × 103 kg/m3) × (9.81 m/s2) × (0.60 m)2 × 1 m

This equation gives us the energy per unit length for a single wave. To get power, we consider energy over time. As waves pass a point with a specific frequency, the power can be calculated by multiplying the energy by the frequency of the waves.

Work is defined as the force acting on an object because it changes a distance. While work is done on an object, the potential energy can be stored in that object. Thus, the relationship between work and energy is direct because the difference in kinetic energy of an object is the work done by the object.

Work done by a force is defined as the product of displacement and the component of force exerted by the object in the direction of displacement, thus when we push a block with some force the body starts moving with some acceleration moves, that's why the work is done.

Some transfer of energy may occur in the method of force where the amount of energy transferred by a force to move an object is called the work done.

Potential energy and work done are the same as kinetic energy and work done because potential energy is a state of the system, a way of storing energy as a property of its configuration or motion, while work is done in most cases there is a way to convert this energy from one body to another which is known as kinetic energy

Thus, Work is defined as the force acting on an object because it changes a distance.

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Answer:

This is likely possible for a region whose matter density is higher than the normal average.

Explanation:

A galaxy is a collection of lumps in space which are clumped together and interact with each other. There are a lot of speculations on how galaxies were birthed. some believe its formed by a collection of massive gas, dust which eventually collapsed under their own gravitational pull. others says its formed by the combination of large lumps of matter which accumulated forming thee galaxies. The possibility of a galaxy forming is dependent on how massive the matter in the region of the universe is.

High density regions in the early universe, referred to as colder spots, eventually evolved into galaxies. The process began with the creation of small galaxies and star clusters followed by massive star formation due to galaxy-galaxy collisions. Over time, the universe developed into the structure we see today.

Regions in the early universe that had higher-than-average density were most likely to become galaxies.

These regions attracted additional matter due to their higher density, and were sometimes referred to as the darkest or 'colder' spots of the early universe.

These colder spots of high density matter were where small galaxies and large star clusters first formed.

In these high density regions: the creation of small galaxies and large star clusters began when the universe was about two percent of its current age.

Galaxy-galaxy collisions in these regions erupted into massive bursts of star formation, some of which led to the formation of black holes.

Over time, clusters and superclusters of galaxies emerged and the universe began to resemble what we see today.

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Answer:

option A

Explanation:

given,

lifting weight = 100 Kg

increase in the weight = 105 Kg

later athlete lift = 200 Kg

Weber's law states that Just noticeable difference of weight is equal to ratio of change to the original.

Just noticeable difference for weight will be

    =[tex]\dfrac{105-100}{100}[/tex]

    = 5 %

since second weight is 200 Kg

so, Just noticeable difference of 200 Kg will be equal to ± 5 % of 200 Kg  which is equal to ± 10 Kg.

now,

Just noticeable difference for 200 Kg

     = 200 + 10 or 200 -10

     = 210 Kg or 190 Kg

Hence, the correct answer is option is option A

Answer:

Explanation:

When a car moves faster then it made suspension to oscillate at a faster rate than the previous frequency. The comfort of the car depends upon the natural frequency of suspension. A low frequency can give discomfort while the high frequency can also be harsh. An optimum frequency matching the level of human comfort is desired in the suspension system to absorb the shock.

The ride is perceived as comfortable when the natural frequency is at the level of 60 to 90 cycles per minute.                      

Answer:

Explanation:

A friend observes only the weather which is different than climate. Weather refers to short term change in the atmosphere while climate refers to what weather is like over a while in a specific area.

The weather may change when we move from one area to another. Cooler weather does not mean that the climate is cooler.

Global warming is the increase in average temperature globally due to which heat is increasing but it does not imply that temperature is hotter everywhere.

Answer: Option c is Correct!

You rub your hands together to keep warm.

Explanation:

First and foremost, mechanical energy is the sum of kinetic energy and potential energy of a system.

M.E = K.E + P.E

Where;

M.E= Mechanical energy

K.E= Kinetic energy

P.E= Potential energy

The kinetic energy is the energy possesed by a moving body, while the Potential energy is possesed by a stationary body.

When you rub your hand together to produce heat that keeps you warm, there is conservation of energy.

According to the first law of thermodynamics also known as the energy conservation law: it states that energy can neither be created nor destroyed, but can be transformed from one form to another.

The rubbing of the hand creates a motion(Kinetic energy) between the palms, this motion is opposed by a force called friction. thus the generation of heat accounts for the transfer of energy from Kinetic to Heat energy, therefore Mechanical energy is conserved according to the law of thermodynamics

Answer:

The number of bulbs = 46 bulbs

Explanation:

Ohm's Law: Ohm's law states that the current flowing through a conductor is directly proportional to its potential difference across its ends. At constant temperature and pressure. It can be expressed mathematically as

V = IR............. Equation 1

making R the subject of formula in equation 1

R = V/I.............. Equation 2

Where R = combined resistance of the several bulbs, V = potential difference, I = current through the circuit.

Given: V= 115 V. I = 2 A.

Substituting these values into equation 2,

R = 115/2

R = 57.5 Ω

Since the bulbs are connected in series,

Number of bulbs = combined resistance/resistance of each bulb

Number of bulbs =  R/Rₙ...................... Equation 3

Where Rₙ = resistance of each bulb, R =combined resistance of the bulb.

Also given: Rₙ = 1.25 Ω, and R = 57.5 Ω

Substituting these values into equation 3

Number of bulbs = 57.5/1.25

Number of bulbs = 46 bulbs.

Therefore the number of bulbs = 46 bulbs

By using Ohm's law to calculate the total resistance of the circuit and dividing it by the resistance of a single bulb, we find that there are 46 light bulbs in the series circuit.

To, calculating the number of light bulbs in a series circuit based on the total resistance of the circuit, which can be found by using Ohm's law. Ohm's law states that the resistance (R) of a circuit can be calculated by dividing the voltage (V) across the circuit by the current (I) through the circuit, which is expressed as R = V/I. Given a 115 V power supply and a current of 2 A, the total resistance of the circuit is R = 115 V / 2 A = 57.5 Ω.

Each light bulb has a resistance of 1.25 Ω, so the number of light bulbs can be calculated by dividing the total resistance by the resistance of a single bulb:

Number of bulbs = Total resistance / Resistance of one bulb

= 57.5 Ω / 1.25 Ω

= 46 bulbs.

Answer:

cars moving at a constant speed on a circular race track.

Explanation:

The rotation of stars in the disk of milky way is more like that of cars moving at a constant speed on a circular race track.

That is all stars are rotating at fixed point in a fixed orbit , such that no two stars are crossing each other. Speed of all stars are different from each other but all stars are rotating at a constant speed.

Answer:

Ceteris Paribus

Explanation:

The process of examining a change in one variable in a model while assuming that all the other variables remain constant is called Ceteris Paribus.

Ceteris Paribus is a Latin phrase that means "all other things being equal" or "all other things held constant" in English. The phrase has found application in disciplines like Economics and Statistics. This phrase as being adopted as a process of examining a change in one variable in a model while assuming that all the other variables remain constant to ascertain the relationship between the variables or make deductions from an experimental study. An example of Ceteris Paribus application is the law of demand and supply in Economics. The law of demand states, Ceteris Paribus, the higher the price, the lower the quantity demanded and vice versa. Conversely, the law of supply states, Ceteris Paribus, the higher price, the higher the quantity supply and vice versa.

The Krebs cycle produces high-energy electrons that are used by the electron transport chain to change ADP into ATP. Through the electron transport chain, high-energy electrons from NADH and FADH2 are transferred from one carrier protein to the next.

An electron is a subatomic particle with a negative charge that can be either attached to or detached from an atom (not bound). Along with protons and neutrons, the electron, which is bonded to the atom, is one of the three major types of particles inside an atom.

Electrons, protons, and neutrons comprise the nucleus of an atom. The protons' positive charge counterbalances the electron's negative charge. The number of protons and electrons in an atom must be equal for it to be in a neutral state.

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Answer:

signal, opening and merge.

Explanation:

As motorists drive onto the acceleration lane, they must get up to the speed limit, signal, find an opening and then merge.

Acceleration lane explanation: an speed variation area or lane of adjustment consisting of additional flooring on the edges of traffic lanes to allow acceleration of vehicles until merging with traffic flow .

Answer:

The total linear momentum at any time is zero.

Explanation:

Hi there!

The momentum of an object is a vector that is calculated by multiplying the mass of the object times its velocity.

The momentum of the system is calculated by adding the momenta of each object that comprise the system (in this case, all the people in Times Square).

Since the people move randomly in all directions, it is most probable that the total momentum of the system is zero because the momentum vectors of people moving in one direction will surely be canceled by the momentum vectors of people moving in the opposite direction. In total, the sum of momentum vectors will be zero (the standing people have null momentum because their velocities are zero).

Final answer:

The total linear momentum of a crowd in Times Square on New Year's Eve can be approximated as zero due to the random and varied movements of the people in the crowd, balancing each other out.

Explanation:

When considering the total linear momentum of a system like the crowd in Times Square on New Year's Eve, we must consider that the system is made up of individuals moving in various directions with different velocities. According to the physical definition of momentum, which is the product of mass and velocity (P = mv), every person has their own momentum. If we assume an idealized situation where movement is random and there is as much motion in one direction as in any other, the total momentum of the system can approximatively be zero at any given instant due to the cancellation of people's momentums in opposite directions. Moreover, because people are not likely to all be moving in the same direction with the same speed at the same time, the net velocity (and thus momentum) of the system may be negligible if averaged over time.

According to Newton's second law in terms of momentum, in the absence of an external force, there would be no change in the total momentum of the system. Therefore, assuming Times Square is a closed system with no significant external forces acting on it, and given the randomness of movement, it can be approximated that the total linear momentum of the crowd is approximately zero.1

Explanation:

They will be alerted of the traffic conditions. They can choose the route according to the weather condition. They will be aware if there is any road construction going on or accident happened. These awareness will save their time and avoid delays. their journey can be more comfortable and less trouble some.

Explanation:

Researching these options time, routes and weather conditions and even more gives the driver ample information about the journey, and places the driver in better position for decision making, with this information and data afore hand he can decides the best route to take should there be any gridlock, he even decides where or not to embark on the journey based on the prevailing weather conditions,

Regarding time of the journey he is well disposed for proper planning and scheduling.

Answer:

Technician A

Explanation:

An oxygen sensor is being tested with a digital multimeter using the MIN/MAX function. The readings are: minimum = 78 mV; maximum = 932 mV; average = 442 mV. Technician A says that the engine is operating normally. Technician B says that the oxygen sensor is skewed too rich. Which technician is correct?

an oxygen sensor detects te amount of oyen in an engine at the exhaust pipe.

if the  oxygen sensor detects oxygen at the above boundary condition, ten the engine is in good working condition

Answer:

[tex]DC=1198.6659\ m[/tex]

Explanation:

Refer the schematic for explanation.

According to the given condition the first cyclist covers 1080 meters eastwards and then travels 1430 meters northwards to reach the camp.

But the second cyclist travels 1950 meters northwards therefore he travelled 520 meters more in the north than the first cyclist.

So, according to the schematic we find the distance DC in the triangle DCE using Pythagoras theorem:

[tex]DC=\sqrt{1080^2+520^2}[/tex]

[tex]DC=1198.6659\ m[/tex]

Explanation:

Car gets 12 miles per gallon uphill and 24 miles per gallon downhill.

Uphill mileage = 12 miles per gallon

Downhill mileage = 24 miles per gallon

Distance to peak = 48 miles.

      Distance to peak = Uphill mileage x Gas used uphill

      48 = 12 x Gas used uphill

      Gas used uphill = 4 gallon

      Distance to peak = Downhill mileage x Gas used downhill

      48 = 24 x Gas used downhill

      Gas used downhill = 2 gallon

Total distance traveled by car = 48 + 48 = 96 miles

Total gas used = 4 + 2 = 6 gallons

Total distance = Mileage x Gas used

96 =  Mileage x 6

Mileage = 16 miles per gallon

The car's gas mileage, in miles per gallon, for the entire trip is 16.

Answer:

16

Explanation:

Final answer:

If a motor neuron involved in a reflex arc is damaged, the event that is least likely to occur is the muscle contraction in response to the sensory stimulus.

Explanation:

If a motor neuron involved in a reflex arc is damaged, the event that is least likely to occur is the muscle contraction in response to the sensory stimulus. In a reflex arc, the motor neuron carries the impulse from the interneuron to the muscle, causing it to contract. If the motor neuron is damaged, this communication pathway is disrupted, and the muscle will not receive the signal to contract.

Answer:

dh/dt=18.75rad/sec

Explanation:

A rocket is launched vertically from a point on the ground. An observer who is 1000 m away from the base of the launching pad, notices that the angle of elevation of the rocket is increasing at a rate of π/40 radians per second when the angle of elevation is π/3.

Find the speed of the rocket at that instant.

you should have a right-angled triangle, where the angle of elevation is Ø, the adjacent is 1000 and the opposite is h, the height of the rocket.

tangent of an angle is opposite over adjacent side

tanØ = h/100 0

h = 1000tanØ

differentiate both sides with respect to dt,change in time

tanØ=sec^2 Ø

dh/dt = 1000sec^2 Ø (dØ/dt)

where Ø = 60° or π/3 rad

dØ/dt = π/40 radians per second

substituting the value into the equation

dh/dt=1000sin^260° *π/40 rad/sec

dh/dt=750*π/40 rad/sec

dh/dt=18.75rad/sec

dh/dt is the same as speed, change in height per time

Answer:

b. Larger for atoms of high atomic number.

Explanation:

The atomic number  of a chemical element is the number of protons found in the nucleus of every atom of that element.

The electrical force between an inner electron and the nucleus of an atom is described by  the Coulomb law

[tex]Fe = \frac{kq_{1}q_{2} }{r^{2}}[/tex]

           where k: Coulomb constant

                       q1 and q2 are the electric charges that interact (in our case  electron and protons)

                       r: Distance between electron and each proton

Then, larger number of protons in the nucleus, more the electrical force will be.

The answer is:

b. Larger for atoms of high atomic number.