Consider a particle with initial velocity v⃗ that has magnitude 12.0 m/s and is directed 60.0 degrees above the negative x axis. 1.What is the x component vx of v⃗ ? 2.What is the y component vy of v⃗ ?

Answer: 5 units

Let's begin by stating clear that movement is the change of position of a body at a certain time. So, during this movement, the body will have a trajectory and a displacement, being both different:

The trajectory is the path followed by the body (is a scalar magnitude).

The displacement is the distance in a straight line between the initial and final position (is a vector magnitude).

According to this, in the description of the object (figure attached) placed at 0 on a number line and moving some units to the left and some oter units to the right, we are talking about the path followed by the object, hence its trajectory. So, 13 units is its trajectory.

But, if we talk about displacement, we have to draw a straight line between the initial position of the object (point 0) to its final position (point 5).

Now, being this an unidimensional problem, the displacement vector for this object is 5 units.

Answer:

A the distance between the positive charge and the electron

B the charge on the electron

D the charge of the positive charge

Explanation:

The electric field produced by the positive charge Q at the location of the electron is given by

[tex]E=k\frac{Q}{r^2}[/tex]

where

k is the Coulomb constant

Q is the charge

r is the distance between the charge Q and the electron

The force exerted on a charged particle by an electric field is given by

[tex]F=qE[/tex]

where q is the magnitude of the charged particle. So, the force exerted on the electron in this problem is

[tex]F=eE = k\frac{eQ}{r^2}[/tex]

where e is the charge of the electron. As we see from the equation, the force depends only the following quantities:

A the distance between the positive charge and the electron (r)

B the charge on the electron (e)

D the charge of the positive charge (Q)

Final answer:

The force on an electron in an electric field depends on the distance between the positive charge and the electron, the charge on the electron, and the charge of the positive charge. Factors such as the masses and radii of the charges do not directly affect the electrostatic force.

Explanation:

An electric field is created by electric charges and can exert a force on other charges within the field. The force on an electron in an electric field created by a positive point charge depends on several factors. Let's identify these dependencies.

A. The distance between the positive charge and the electron: The force is inversely proportional to the square of the distance between the charges (r2).

B. The charge on the electron: The electrostatic force exerted on the electron is proportional to the magnitude of its charge.

D. The charge of the positive charge: The magnitude of the electric field, and therefore the force on the electron, is proportional to the charge of the positive point charge (Q).

The mass of the electron (C), the mass of the positive charge (E), the radius of the positive charge (F), and the radius of the electron (G) do not affect the electrostatic force the electron experiences.

Answer:

Of longitudinal waves

Explanation:

Depending on the direction of the oscillation, there are two types of waves:

- Transverse waves: in a transverse wave, the oscillations occur perpendicularly to the direction of propagation of the wave. Examples are electromagnetic waves.

- Longitudinal waves: in a longitudinal wave, the oscillations occur parallel to the direction of propagation of the wave. In such a wave, the oscillations are produced by alternating regions of higher density of particles, called compressions, and regions of lower density of particles, called rarefactions. Examples of longitudinal waves are sound waves.

Compressions and rarefactions are characteristic of sound waves, which are longitudinal waves. Compressions are regions of high pressure, while rarefactions are regions of low pressure, both created by the vibrating motion of the sound source.

Compressions and rarefactions are characteristic features of a sound wave, which is a type of longitudinal wave. When a sound source vibrates, it causes fluctuations in the pressure of the medium through which it travels, typically air. These fluctuations manifest as alternating regions of higher pressure, known as compressions, and lower pressure, known as rarefactions. Sound waves consist of these repeating patterns of compressions and rarefactions, moving away from the source of the sound in the form of a wave.

During compression, air molecules are pushed closer together, leading to a higher pressure region. Conversely, during rarefaction, air molecules are spread out, creating a lower pressure region. For example, when a speaker cone moves forward, it compresses the air in front of it, and when it moves backward, it creates a rarefaction. These disturbances travel through the air, causing our eardrums to vibrate and enabling us to perceive sound.

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The term is “ISOTOPES” These describe atoms with different atomic masses.

The term which describes different atomic masses of similar atom because of varying numbers of neutrons are Isotopes.

Explanation:

The isotopes are the chemical element which has different atomic masses due to the fact that number of neutrons are not same but it has same number of proton.

When the number of neutron increases in a nucleus, with the same electronic configuration and same number of proton, element is said to have isotopes. There are may be variants of isotopes of an element. For example, hydrogen has 3 isotopes.

Answer:

Explanation:

The atmosphere is the gaseous portion of the earth. It consists of different molecules of gas.

The geosphere is the solid portion of the earth which include the crusts, mantle and the core.

Earth is a dynamic planet. Our planet is dynamic in the sense that it is constantly changing and all its parts interacts with one another.

The gases in the atmosphere such a CO₂, H₂O, Nitrogen oxides originates from volcanic processes from deep within the earth. Hydrothermal vents and black smokers constantly release gases into the atmosphere.

The atmosphere plays a lot of roles in determining weather and climatic conditions. Agents of denudation like wind, water and glaciers are connected to the movement of gaseous portion of the earth. As new rocks forms on the crust, wind, water and glaciers acts on them. This process plays a central role in the rock cycle. The rock cycle would not be complete without agents of denudation which are strongly connected to the workings of atmospheric gases and materials like dusts.  

Therefore we see that the geosphere and atmosphere are linked.

Answer: [tex]90\°[/tex]

Explanation:

The Compton Shift [tex]\Delta \lambda[/tex] in wavelength when the photons are scattered is given by the following equation:

[tex]\Delta \lambda=\lambda_{c}(1-cos\theta)[/tex]     (1)

Where:

[tex]\lambda_{c}=2.43(10)^{-12} m[/tex] is a constant whose value is given by [tex]\frac{h}{m_{e}c}[/tex], being [tex]h[/tex] the Planck constant, [tex]m_{e}[/tex] the mass of the electron and [tex]c[/tex] the speed of light in vacuum.

[tex]\theta)[/tex] the angle between incident phhoton and the scatered photon.

We are told the maximum Compton shift in wavelength occurs when a photon isscattered through [tex]180\°[/tex]:

[tex]\Delta \lambda_{max}=\lambda_{c}(1-cos(180\°))[/tex]     (2)

[tex]\Delta \lambda_{max}=\lambda_{c}(1-(-1))[/tex]    

[tex]\Delta \lambda_{max}=2\lambda_{c}[/tex]     (3)

Now, let's find the angle that will produce a fourth of this maximum value found in (3):

[tex]\frac{1}{4}\Delta \lambda_{max}=\frac{1}{4}2\lambda_{c}(1-cos\theta)[/tex]      (4)

[tex]\frac{1}{4}\Delta \lambda_{max}=\frac{1}{2}\lambda_{c}(1-cos\theta)[/tex]      (5)

If we want [tex]\frac{1}{4}\Delta \lambda_{max}=\frac{1}{2}\lambda_{c}[/tex], [tex]1-cos\theta[/tex]   must be equal to 1:

[tex]1-cos\theta=1[/tex]   (6)

Finding [tex]\theta[/tex]:

[tex]1-1=cos\theta[/tex]

[tex]0=cos\theta[/tex]  

[tex]\theta=cos^{-1} (0)[/tex]  

Finally:

[tex]\theta=90\°[/tex]    This is the scattering angle that will produce [tex]\frac{1}{4}\Delta \lambda_{max}[/tex]      

-- turbulence

-- well mixed, non layered atmosphere

-- tornados

-- cumulonimbus clouds

-- thunderstorms

-- a lot of heavy clouds

When half of one of the charges of equal magnitude is transferred to the other, the electric force between them reduces to 75% of the original force while maintaining the same distance.

In this scenario, you're dealing with the concept of electric forces between charged particles. The force between two charges is given by Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This can be represented by the equation F = k * Q1 * Q2 / r^2

Initially, we have two charges both of magnitude Q, the force is F_initial = k * Q * Q / r^2. Half of one of the charges is transferred to the other, the charges become 1.5Q and 0.5Q. The new force is F_final = k * 1.5Q * 0.5Q / r^2 = 0.75 k * Q * Q / r^2.

So, the force between the charges reduces to 75% of the original force when half of one of the charges is transferred to the other while the distance remains the same.

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Answer:

4 seconds

Explanation:

Average acceleration is change in velocity over change in time:

a = Δv / Δt

Δt = Δv / a

Δt = (15 m/s - 5 m/s) / 2.5 m/s²

Δt = 4 s

Answer: The time taken by the bicycle rider is 4 seconds.

Explanation:

To calculate the time taken by the rider, we use first equation of motion:

[tex]v=u+at[/tex]

where,

v = final velocity of the rider = 15 m/s

u = initial velocity of the rider = 5 m/s

a = acceleration of the car = [tex]2.5m/s^2[/tex]

t = time taken = ?

Putting values in above equation, we get:

[tex]15=5+(2.5\times t)\\\\t=\frac{15-5}{2.5}\\\\t=4s[/tex]

Hence, the time taken by the bicycle rider is 4 seconds.

In convex mirrors the focus is virtual and the focal distance is negative. This is how the reflected rays diverge and only their extensions are cut at a point on the main axis, resulting in a virtual image of the real object .

The Mirror equation is:  

[tex]\frac{1}{f}=\frac{1}{u}+\frac{1}{v}[/tex]    (1)  

Where:  

[tex]f=-6cm[/tex] is the focal distance  

[tex]u=12cm[/tex] is the distance between the object and the mirror  

[tex]v[/tex] is the distance between the image and the mirror

We already know the values of [tex]f[/tex] and [tex]u[/tex], let's find [tex]v[/tex] from (1):  

[tex]v=\frac{u.f}{u-f}[/tex]    (2)  

[tex]v=\frac{(12cm)(-6cm)}{12cm-(-6cm)}[/tex]

[tex]v=-4cm[/tex]   (3)

On the other hand, the magnification [tex]m[/tex] of the image is given by the following equations:  

[tex]m=-\frac{v}{u}[/tex]   (4)

[tex]m=\frac{h_{i}}{h_{o}}[/tex]   (5)

Where:

[tex]h_{i}[/tex] is the image height  

[tex]h_{o}=15cm[/tex] is the object height

Now, if we want to find the image height, we firstlu have to find [tex]m[/tex] from (4), substitute it on (5) and find [tex]h_{i}[/tex]:

Substituting  (3) in (4):

[tex]m=-\frac{-4cm}{12cm}[/tex]  

[tex]m=\frac{1}{3}[/tex]    (6)

Substituting  (6) in (5):

[tex]\frac{1}{3}=\frac{h_{i}}{15cm}[/tex]

[tex]h_{i}=\frac{15cm}{3}[/tex]

Finally we obtain the value of the height of the image produced by the mirror:

[tex]h_{i}=5cm[/tex]

Answer:

The answer is D. on edgen

Explanation:

D. 5.0

Answer: acceleration will increase

According to newtons second law the relationship between the force on an object and the acceleration and an object

Answer:

Amygdala, Frontal cortex

Explanation:

The amygdala is part of the brain responsible for aggressive behavior, fear and immediate reactions associated with high risks. The frontal cortex, on the other hand, is the part of the brain responsible for reasoning. Because the former matures faster than the latter in adolescents, then teens' behavior is generally associated with high risks and little reasoning before acting.

The principal quantum number, identified by n, gives information about the orbital energy level of the electron.

To understand it better:

According to the current model of the atom, it has a central nucleus with electrons orbiting around. These orbits are located at different energy levels that are related to the distance from the electron to the nucleus.

So, the first energy level, is considered the lowest, because it is the smallest and the one that is in average closer to the nucleus, and as n increases, the farther away from the nucleus is the orbital and therefore more energy the electron has.

It should be noted that the values ​​of n will always be positive integer numbers, for example: 1, 2, 3, 4, 5, 6,7. Although theoretically its value oscillates between 1 and infinity, until now only atoms whose maximum energetic level is 8 are known.

Answer:

The size

Explanation:

(A) 3.9

When a dielectric is inserted between the plates of a capacitor, the capacitance of the capacitor increases according to the equation:

[tex]C' = k C[/tex] (1)

where

C' is the final capacitance

k is the dielectric constant

C is the original capacitance

The capacitance is inversely proportional to the to voltage across the plates:

[tex]C=\frac{Q}{V}[/tex] (2a)

where Q is the charge stored and V the potential difference across the plates. We can rewrite C' (the capacitance of the capacitor filled with dielectric) as

[tex]C'=\frac{Q}{V'}[/tex] (2b)

Substituting (2a) and (2b) into (1), we find

[tex]V'=\frac{V}{k}[/tex] (3)

where

V = 45.0 V is the original voltage across the capacitor

V' = 11.5 V is the voltage across the capacitor filled with dielectric

Solving for k,

[tex]k=\frac{V}{V'}=\frac{45.0 V}{11.5 V}=3.9[/tex]

(B) 22.8 V

When the dielectric is partially pulled away, the system can be assimilated to a system of 2 capacitors in parallel, of which one of them is filled with dielectric and the other one is not.

Keeping in mind that the capacitance of a parallel-plate capacitor is proportional to the area of the plates:

[tex]C \propto A[/tex]

and in this case, the area of the capacitor filled with dielectric is just 1/3 of the total, we can write:

[tex]C_1 = \frac{2}{3}C\\C_2 = \frac{1}{3}kC[/tex]

where C1 is the capacitance of the part non-filled with dielectric, and C2 is the capacitance of the part filled with dielectric. The total capacitance of the system in parallel is

[tex]C'=C_1 + C_2 = \frac{2}{3}C+\frac{1}{3}kC=(\frac{2}{3}+\frac{1}{3}k)C[/tex]

Substituting,

[tex]C'=(\frac{2}{3}+\frac{1}{3}(3.9))C=1.97 C[/tex]

This is equivalent to a capacitor completely filled with a dielectric with dielectric constant k=1.97. Therefore, using again eq.(3), we find the new voltage:

[tex]V'=\frac{V}{k}=\frac{45.0 V}{1.97}=22.8 V[/tex]

Answer: It seems i am made for this since, i LOVE eclipses, so basically it's when the moon goes in front of the moon, and is kinda hidden, making an eclipse

Hello There!

A partial solar eclipse is when the moon comes between the sun and our planet "Earth" but they do not align in a perfect straight line. Because of this, the moon only covers around half of the suns disc

A nuclear reaction will not be affected with the use of a catalyst.

The incorrect statement is that the rate of a nuclear reaction is increased by the addition of a catalyst. Nuclear reactions result in significant energy changes and the transformation of elements or isotopes, but they are not influenced by catalysts or the chemical state of atoms.

One of the statements about nuclear reactions provided in the student's question is not true. In fact, the statement that the rate of a nuclear reaction is increased by the addition of a catalyst is incorrect. Unlike chemical reactions, the rate of a nuclear reaction is not affected by catalysts because nuclear reactions involve changes within the nucleus of an atom, and catalysts do not have the ability to affect the nuclear forces that govern these reactions.

Nuclear reactions are significant because they involve much larger energy changes compared to ordinary chemical reactions. The energy released or absorbed during nuclear reactions can result in a measurable change in mass, according to the principle of mass-energy equivalence. Also, these reactions often lead to the formation of different isotopes or even different elements, depending on the changes within the atomic nucleus.

Furthermore, nuclear reactions are not influenced by the chemical state of the atoms involved or by the presence of a catalyst. They depend primarily on factors related to the nuclei themselves, such as neutron flux in a fission reactor or temperature and pressure in a fusion reaction.

The path difference between the two waves is the path difference between the two waves should be one and one-quarter of a wavelengths.

Wavelength is the distance between two identical or similar positions it means that it is the distance between crests or trough in the adjacent cycle of the waveform.

Wavelength is denoted by (lambda).

It is measured in meter, or centimeter, or millimeters.

Mathematically,

Wavelength is equal to velocity divided by frequency,

So,

Wavelength (lambda) = Velocity/frequency.

Velocity is in meter per second.

Frequency is in 1/second.

Prism is a transparent object in which if  sunlight is passed then it will be split in a VIBGYOR

where V = vilot, I = indigo, B = blue, G = green, Y = Yellow, O = orange, R = red.

In this series wavelength of red is higher and vilot is smaller and frequency of violet is higher and red is smaller.

Therefore, The path difference between the two waves is the path difference between the two waves should be one and one-quarter of a wavelengths.

Learn more about wavelength here:

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Answer:

A

Explanation:

First of all the answer is less than the smallest resistor, so it is less than 18 ohms.

1 / r1 + 1/ r2 = 1/r

1/18 + 1/23.5 = 1/r

1/18 = 0.05555555

1/23.5 = 0.0422532

1/18 + 1/23.5 = 0.0555555 + 0.0422532

1/r = 0.0981087  

r = 1/0.0981087

r = 10.193

A

Final answer:

The equivalent resistance for two resistors in parallel, one with 18.0 ohms and the other with 23.5 ohms, is approximately 10.2 ohms, which is answer choice A.

Explanation:

When calculating the equivalent resistance for resistors in parallel, you use the formula 1/Req = 1/R1 + 1/R2 where Req is the equivalent resistance, and R1 and R2 are the resistances of the individual resistors. For the two resistors with resistances of 18.0 ohms and 23.5 ohms, the calculation would be:

1/Req = 1/18.0 + 1/23.5

1/Req = 0.0556 + 0.0426

1/Req = 0.0982

Req = 1 / 0.0982

Req ≈ 10.18 ohms

Therefore, the correct answer is A. 10.2 ohms.

Answer:

A. The wires will be arranged in order of increasing resistance.

Explanation:

The resistance of a wire is given by

[tex]R=\frac{\rho L}{A}[/tex]

where

[tex]\rho[/tex] is the resistivity of the material

L is the length of the wire

A is the cross-sectional area of the wire

In this problem we have several wires made of the same material (so, same [tex]\rho[/tex]) and same length (same L): so, the only quantity that changes is their thickness, so their value of A.

We see from the formula that the resistance R is inversely proportional to the cross-sectional area A: therefore, the smaller the value of A, the larger the value of R. This means that if we arrange the wires in order of decreasing thickness, we are arranging the wires in order of increasing resistance.

Answer:

c) ability to store charge

Explanation:

The capacity of an object gives a measure of the ability of the object to store electric charge. In formula, it is defined as the ratio between the charge stored on the object and the electric potential on the object:

[tex]C=\frac{Q}{V}[/tex]

where

Q is the charge

V is the voltage

Therefore, an object with a larger capacity than another object means that if the two objects are at same voltage V, the first object can store more charge than the second object.

Capacitance measures an object's ability to store charge, and is dependent on the geometry of conductor arrangement and the dielectric properties between conductors. It is measured in farads, with one farad being equivalent to one coulomb of charge per one volt.

The property of objects that is best measured by their capacitance is their ability to store charge. A capacitor, which is an arrangement of objects that can store electrical energy due to their geometry, has a capacitance that is directly proportional to the electric potential energy it can store per unit electric potential. The capacitance of a system depends only on the geometry of the conductor arrangement and the physical properties of the dielectric between the conductors.

It is important to note that capacitance is not related to a material's ability to conduct electric current nor is it primarily about distorting an external electrostatic field. Instead, it defines how much charge can be separated for a given electric potential, that is, how much electric energy is stored or held in potential. The SI unit of capacitance is the farad (F), where 1 farad equals 1 coulomb (C) per 1 volt (V).

Answer:

Tundra Biome

Explanation:

Permafrost is a type of soil that is frozen all year round. It consists of rocks, soils and ice. The ice or frost holds the earth materials together.

The tundra biome lies below the arctic circle close to the north pole. Most of the earth here is predominantly frozen all year round. A layer of glacier covers  the surface and a deep lying layer of permafrost follows suit.

Some mountain tops capped with ice shows this tundra features.

Most tundras are termed cold deserts as they have little to no precipitation all year round. There is absence of vegetation cover as a result of low growing season of the plants.  

Answer:

[tex]160 kg/m^3[/tex]

Explanation:

The density of the liquid is given by:

[tex]d=\frac{m}{V}[/tex]

where

m is the mass of the liquid

V is its volume

The mass of the liquid is

m = 1.0 kg

while the volume is the volume of a cylinder with height h=0.20 m and radius r=0.10 m:

[tex]V=\pi r^2 h = \pi (0.10 m)^2 (0.20 m)=6.28\cdot 10^{-3} m^3[/tex]

So, the density is

[tex]d=\frac{1.0 kg}{6.28\cdot 10^{-3} m^3}=159.2 kg/m^3 \sim 160 kg/m^3[/tex]

Answer:

4.71 eV

Explanation:

For an electromagnetic wave with wavelength

[tex]\lambda=264 nm = 2.64\cdot 10^{-7} m[/tex]

the energy of the photons in the wave is given by

[tex]E=\frac{hc}{\lambda}=\frac{(6.63\cdot 10^{-34}Js)(3\cdot 10^8 m/s)}{2.64\cdot 10^{-7}m}=7.53\cdot 10^{-19} J[/tex]

where h is the Planck constant and c the speed of light. Therefore, this is the minimum energy that a photon should have in order to extract a photoelectron from the copper surface.

The work function of a metal is the minimum energy required by the incident light in order to extract photoelectrons from the metal's surface. Therefore, the work function corresponds to the energy we found previously. By converting it into electronvolts, we find:

[tex]E=\frac{7.53\cdot 10^{-19} J}{1.6\cdot 10^{-19} J/eV}=4.71 eV[/tex]

Answer:

d) 182 mm Hg

Explanation:

The ratio of partial pressure to total pressure is equal to the molar ratio.

P / 870 mm Hg = 0.21

P = 182 mm Hg

Answer is D.

Final answer:

At  an atmospheric pressure of 870 mm Hg with 21 percent oxygen, the partial pressure of oxygen is D) 182mm

Explanation:

The question is asking to calculate the partial pressure of oxygen in the atmosphere when the total atmospheric pressure is 870 mm Hg, given that oxygen constitutes 21% of the atmosphere. The partial pressure of oxygen (Po₂) is found by multiplying the total pressure by the percent content of oxygen in the mixture. This can be calculated as follows:

Po₂ = (870 mm Hg) × (0.21)

Therefore, the partial pressure of oxygen is:

Po₂ = 182.7 mm Hg

Since we only have whole numbers in the options provided, we round this to the nearest whole number, which is 183 mm Hg. This is not exactly one of the options given, so it seems there might be a typo in the choices; the closest correct answer would be 182 mm Hg.

Answer:

False

Explanation:

A bloody footprint or a fingerprint would be considered a transfer stain.A transfer stain is one which occurs from an object coming into contact with already existing bloodstains and will leave swipes transfers behind.A passive stain is one that results from a blood drop,blood flow or blood pool.

Answer:

[tex]2.68\cdot 10^8 MJ[/tex]

Explanation:

The power is related to the energy by

[tex]P=\frac{E}{t}[/tex]

where

P is the power

E is the energy

t is the time elapsed

The power of this nuclear power planet is

[tex]P=3100 MW = 3.1\cdot 10^9 W[/tex]

The time we are considering is 1 day, which is

[tex]t = 1 d = 86400 s[/tex]

So we can re-arrange the previous equation to find the energy produced by the power plant in one day:

[tex]E=Pt =(3.1\cdot 10^9 W)(86400 s)=2.68\cdot 10^{14} J=2.68\cdot 10^8 MJ[/tex]

The answer is false , because they move without an electromagnetic

Answer: False

Explanation:

Answer:

B) 2 times what it now is

Explanation:

The acceleration due to gravity at the surface of the Earth is given by

[tex]g=\frac{GM}{R^2}[/tex]

where

G is the gravitational constant

M is the mass of the Earth

R is the Earth's radius

In this problem, the mass of the Earth is doubled:

M' = 2M

while the radius remains the same:

R' = R

so the new acceleration due to gravity would be

[tex]g'=\frac{GM'}{R'^2}=\frac{G(2M)}{R^2}=2\frac{GM}{R^2}=2g[/tex]

so, the acceleration due to gravity would become twice the current value.

Note also that the value of g does not depend on the mass of the objects involved.

4)Both B and D.This happens becaus3 at the ceryain time, A experiences a flood tide causing the waters to come near it.And since B and D are the closest coastlines they are affected the most.

Answer:

800 kg/m³

Explanation:

I assume you want to find the density of the sphere?

Start with a free body diagram.  There are three forces acting on the sphere: gravity pulling the sphere down, buoyancy pushing the sphere up, and tension pulling the sphere down.

Applying Newton's second law:

∑F = ma

B - W - T = ma

Since the sphere isn't accelerating, a = 0.

B - W - T = 0

B = W + T

We know that the tension is one-fourth the weight:

B = W + W/4

B = 5/4 W

B = 5/4 mg

Buoyant force is defined as:

B = ρVg,

where ρ is the density of the fluid, V is the displaced volume, and g is acceleration of gravity.

ρVg = 5/4 mg

ρV = 5/4 m

The mass of the sphere is equal to its density times its volume.  Since the sphere is fully submerged, it's volume is the same as the volume of the displaced water.

ρV = 5/4 ρₓV

ρ = 5/4 ρₓ

ρₓ = 4/5 ρ

So the density of the sphere is 4/5 the density of the water.  Water's density is 1000 kg/m³, so:

ρₓ = 4/5 (1000 kg/m³)

ρₓ = 800 kg/m³

The submerged sphere experiences a gravitational force (its weight) and a counteracting buoyant force. The tension in the string tethering it is one-fourth of the sphere's weight. This situation could occur if the buoyant force on the sphere is three-fourths of the sphere's weight.

The subject of this question is about the physics of forces in a fluid medium - specifically, the interaction between buoyancy, weight, and tension. In this case, a sphere is fully submerged in water and secured with a string. Despite being underwater, the object still experiences the force of gravity, which pulls it downward. This weight is represented by the mass of the sphere times the acceleration due to gravity (we use 9.8 m/s² for Earth).

However, while submerged, the sphere also experiences a buoyant force due to the displacement of the water. This force is equal to the weight of the water displaced by the sphere, which acts in the opposite direction of the weight, or upward. The string provides a tension force that prevents the sphere from moving.

In this scenario, the tension force in the string is one-fourth the weight of the sphere. This could happen if the buoyant force acting on the sphere is equal to three-fourths of the sphere’s weight, leaving one-fourth of the sphere's weight to be balanced by the string.

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