if the expression for the electric potential due to a small sphere of charge q at point p that is a distance d from the center of a small sphere is kqd , then the electric potential at a point o that is a distance 2d from the center of the small sphere is?

The net gravitational force is terms of L and h and is equal to[tex]f_{net} = G m_3*(m_2 / ((L - 1)^2 + h^2) + m_1 / (L^2 + h^2))[/tex]

(a) The gravitational force on the Moon due to the Earth can be calculated using the equation:

f_gravity = G * (m2 * m3) / d^2

where d is the distance between the Earth and the Moon. The distance between the Earth and the Moon can be calculated using the Pythagorean theorem:

d = sqrt((L - 1)^2 + h^2)

Plugging in the values, we get:

[tex]f_{gravity} = G * (m_{Earth} * m_{Moon}) / d^2 = G * (m_{2} * m_{3}) / d^2 \\\\= G * (m_{2} * m_{3}) / (sqrt((L - 1)^2 + h^2))^2[/tex]

(b) The gravitational force on the Moon due to the Sun can be calculated using the same equation as above:

f_gravity = G * (m1 * m3) / d^2

where d is the distance between the Sun and the Moon. The distance between the Sun and the Moon can be calculated using the Pythagorean theorem:

d = sqrt(L^2 + h^2)

Plugging in the values, we get:

[tex]f_{gravity} = G * (m_{Sun} * m_{Moon}) / d^2 \\= G * (m_{1} * m_{3}) / d^2 = G * (m_{1} * m_{3}) / (sqrt(L^2 + h^2))^2[/tex]

(c) The net gravitational force on the Moon is the sum of the gravitational forces due to the Earth and the Sun:

f_net = f_gravity_Earth + f_gravity_Sun

Substituting the values of f_gravity_Earth and f_gravity_Sun, we get:

[tex]f_{net} = G * (m_2 * m_3) / (sqrt((L - 1)^2 + h^2))^2 + G * (m_1 * m_3) / (sqrt(L^2 + h^2))^2[/tex]

[tex]f_{net} = G * (m_2 * m_3) / ((L - 1)^2 + h^2) + G * (m_1 * m_3) / (L^2 + h^2)[/tex]

[tex]f_{net} = G m_3*(m_2 / ((L - 1)^2 + h^2) + m_1 / (L^2 + h^2))[/tex]

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Answer:

9.22 m=s

Explanation:

m=s×v

jskkdkdjdhbdnkksksijsj

jdjkdo

To lift the object, you must apply a force of 27 Newtons (9 Newtons divided by 3, the mechanical advantage).

The equation you can use to find the answer is MA = F0/Fi, where MA is the mechanical advantage, F0 is the input force and Fi is the output force.

MA is the mechanical advantage of a machine and is the ratio of output force to input force. For example, if an object needs to be lifted but the force required to lift it is too great, a machine such as a pulley system can be used to reduce the force needed. A pulley system has a mechanical advantage of 3, meaning that the output force is three times greater than the input force.

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The following factors change as one moves to higher magnifications with a microscope:

What is magnification?

Magnification is a measure of how much an image is enlarged or increased in size compared to the original object. It is commonly used in optics, such as microscopes and telescopes, to describe the level of enlargement achieved by the instrument. The magnification is usually expressed as a ratio or a multiple of the original size.

a. Resolution: Resolution refers to the ability of a microscope to distinguish two separate points as separate entities. As one moves to higher magnifications, the resolution of the microscope increases, meaning that smaller and finer details can be seen.

b. Amount of light needed: As magnification increases, the amount of light needed to illuminate the specimen also increases. This is because the increased magnification reduces the amount of light that reaches the specimen and the observer.

c. Working distance: Working distance refers to the space between the lens and the specimen. As one moves to higher magnifications, the working distance decreases, meaning that the lens must be positioned closer to the specimen.

d. Depth of field: Depth of field refers to the range of distances from the lens that are in focus at any given time. As one moves to higher magnifications, the depth of field decreases, meaning that only a very small portion of the specimen will be in focus at any given time.

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It has been demonstrated that the angle when the body exits the sphere is   θ = cos⁻¹(2/3)

Between two surfaces that are sliding or attempting to slide over one another, there is a force called friction. For instance, friction makes it challenging to push a book down the floor. Every time an object moves or attempts to move, friction always acts in the direction opposing to that movement.

Force acting on a stationary particle

The following formula is used to compute the particle's force while it is stationary;

Rgcos = mgcos = mv2/R v2 —- (1)

power-saving measures

Utilizing the principle of energy conservation, one may calculate the object's ultimate speed once it begins to slide.

v2 = 1/2mR(1 - cos) = 2gR(R - Rcos) ---(2) reconcile (1) and (2)

Rgcos = 2gR (cos - 1);

cos = 2 - cos 2.

Cos1(2/3) = 3cos = 2cos = 2/3

As a result, the body exits the sphere at an angle of θ = cos⁻¹(2/3) , proved.

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The complete question is

A body of mass m and negligible size starts from rest and slides down the surface of a frictionless solid sphere of radius R. Prove that the body leaves the sphere when 0 = cos(2/3).

Answer:

15.33 m/s

Explanation:

We are here given that ,

As we know that,

[tex]\longrightarrow R = \dfrac{u^2\sin2\theta}{g} \dots (1)\\[/tex]

And ,

[tex]\longrightarrow h =\dfrac{u^2\sin^2\theta}{2g} \dots (2)\\[/tex]

Divide equation 1 and 2 ,

[tex]\longrightarrow \dfrac{R}{h}=\dfrac{4 \cos\theta}{\sin\theta} \\[/tex]

[tex]\longrightarrow \dfrac{24m}{6m}=4 \cot\theta \\[/tex]

[tex]\longrightarrow \cot\theta = 1 \\[/tex]

[tex]\longrightarrow \theta = \cot^{-1}(1) \\[/tex]

[tex]\longrightarrow \underline{\underline{\theta = 45^{\circ}}}\\[/tex]

Now we may substitute this value in equation 1 as ,

[tex]\longrightarrow 24 =\dfrac{ u^2\sin(2\times 45^{\circ} )}{g} \\[/tex]

[tex]\longrightarrow 24g = u^2\sin90^\circ \\[/tex]

[tex]\longrightarrow u^2 = 24 \times 9.8 \\[/tex]

[tex]\longrightarrow u =\sqrt{235.2} m/s \\[/tex]

[tex]\longrightarrow \underline{\underline{ u \approx 15.33 \ m/s }}\\[/tex]

and we are done!

At a height of 4.48 meters, a rock's kinetic energy is twice its potential energy.

Potential energy is the energy stored in any object or system due to the position or arrangement of its parts. It is, however, unaffected by factors outside of the object or system, such as air or height. Kinetic energy, on the other hand, is the energy of moving particles in an object or system.

Given that a 6.0-kg rock is dropped from a height of 9.0 m.

Calculate the total potential energy at the initial point,

PE = mgh

PE = 6 x 9.81 x 9

PE = 530.74 J

At the zero height, the kinetic energy will be maximum and is equal to the total energy,

KE = 530.75 J

1/2 mv² = 530.75

v² = 175.85

The height at which the kinetic energy is two times the potential energy is calculated as:-

1 /2 x mv² = 2 x mgh

h = ( 4 v²) / ( 4 x 9.81 )

h = 4 ( 175.82 ) / ( 4 x 9.81 )

h = 4.48 meters

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The device used to vary the current in a circuit is a variable resistor. The symbol of a variable resistor is option d. The symbol with a rectangle and an arrow.

A variable resistor also called a rheostat  is a resistor of which the electric resistance value can be adjusted. A variable resistor is in essence an electro-mechanical transducer and normally works by sliding a contact (wiper) over a resistive element.

When a variable resistor is used as a potential divider by using 3 terminals it is called a potentiometer.

When only two terminals are used, it functions as a variable resistance and is called a rheostat. Electronically controlled variable resistors exist, which can be controlled electronically instead of by mechanical action. These resistors are called digital potentiometers.

Here, the resistance thereby the current through the lamp 2 can be varied by placing a resistor. Hence, option d is correct.

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The symbol used in diagram to represent the device is rheostat's symbol.

Correct option is D.

Electric current is defined as the rate of flow of electrons in a conductor. The SI Unit of electric current is the Ampere.

In given circuit,

A device is added to the electrical circuit to vary the current in Lamp 2 only,

Electrical current is varied by applying variable resistance,

The device used to apply variable resistance is rheostat, which has symbol of box with an arrow through it.

Hence, rheostat's symbol will be used in diagram to represent the device.

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Answer:

3Ω

Explanation:

we are here given that,

From Ohm's law , we know that,

[tex]\implies V = iR \\[/tex]

where ,

on substituting the respective values, we have,

[tex]\implies 12V = 4A(R) \\[/tex]

[tex]\implies R =\dfrac{12V}{4A} \\[/tex]

[tex]\implies \underline{\underline{ R = 3\Omega}} \\[/tex]

and we are done!

The correct relationship between T and P is represented by option B)

T = P.

The net force operating on the system is represented by the tension in the wire T, which is equal to the total of the forces acting on each weight. Because only the gravitational force and the tension force are operating on each weight in this situation, the net force exerted on each weight is equal to the difference between the tension and the weight. T must therefore equal the sum of the gravitational pull P and the forces acting on each weight.

Since m represents the mass of each weight and g is the acceleration brought on by gravity, the equation for the relationship between T and P must be T = P + m * g.

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The arrow pointing downward is gravitational force, F(g), The left arrow is the applied force, F(t), The right arrow is frictional force, F(f) and the arrow pointing upward is the net force, F(n).

A force is a push or pull upon an object resulting from the object's interaction with another object. Forces can cause an object to accelerate or change its direction of motion.

Forces can be described by their magnitude and direction. In physics, forces can be caused by many interactions, including gravity, electromagnetic forces, and the strong and weak nuclear forces.

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The height of the jump having a mass of 67kg with the vertical velocity of 6.4m/s is 2.089m.

Potential energy is defined as the energy stored in an object or system by virtue of its position or arrangement of parts while kinetic energy is defined as the energy of the moving particles of an object or system.

Potential energy is represented as :

P.E.= mgh

Kinetic energy  is represented as :

[tex]K.E.= 1/2mv^2[/tex]

where, m = mass of the object

h= height

v= velocity

g= acceleration due to gravity which is [tex]9.8m/s^2[/tex]

For above given example,

m= 67kg, v= 6.4m/s

we first find out Kinetic energy,

K.E.=[tex]\frac{1}{2} 67* (6.4)^2[/tex]= 2744.32/2= 1372.16 J

As we know, K.E.= P.E.

So, P.E.= 1372.16J = mgh

1372.16= 67* 9.8* h

height= 2.089 m

Thus, the height of the jump having a mass of 67kg with the vertical velocity of 6.4m/s is 2.089m.

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From a towering building, 2 tennis balls fall into the air. Lead pellets are contained within one of them. The lead-filled ball becomes the first to touch the ground.

The invisible atmospheric mixture that envelops Earth is called air. Most organisms depend on vital elements like oxygen and nitrogen to thrive, which are found in air. Of course, a member of this species is human people (Homo sapiens). In some cases, "atmosphere" is substituted in place of "air."

Respiration is a procedure that includes breathing. A living organism breathes by taking intake oxygen from the environment and exhaling carbon dioxide. This process provides the energy necessary for plants and animals to absorb, grow, and sustain life.

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Answer:

C) 0.83 Ω

Explanation:

Answer:

see below

Explanation:

We are here given that ,

As we know that,

[tex]\implies h =\dfrac{u^2\sin^2\theta}{2g} \\[/tex]

substitute the respective values,

[tex]\implies 2.4 m =\dfrac{u^2\sin^245^\circ}{2\times 10} \\[/tex]

[tex]\implies 2.4m =\dfrac{u^2\times \bigg(\dfrac{1}{\sqrt2}\bigg)^2}{20}\\[/tex]

[tex]\implies u^2 = 40 \times 2.4 = 96 \\[/tex]

[tex]\implies u^2 =\sqrt{96}\\[/tex]

[tex]\implies \underline{\underline{ u \approx 9.79 \ m/s }}\\[/tex]

secondly we know that,

[tex]\implies t = \dfrac{u\sin\theta}{g}\\[/tex]

[tex]\implies t =\dfrac{9.79\times \sin45^\circ}{10} \\[/tex]

[tex]\implies t =\dfrac{9.79\times \dfrac{1}{\sqrt2}}{10} \\[/tex]

[tex]\implies \underline{\underline{ t \approx 0.69 \ s }}\\[/tex]

and we are done!

Answer:

Explanation:

Matter is identified based on its physical and chemical properties.

Physical properties, such as color, texture, density, melting point, and boiling point, can be used to identify matter without changing its composition. For example, a solid object with a high density and a high melting point is likely to be a metal, while a lighter, less dense material with a low melting point is likely to be a plastic.

Chemical properties, such as reactivity, flammability, and acidity, are also used to identify matter. For example, the reaction of a substance with a strong acid or base can provide information about its chemical composition.

In addition to physical and chemical properties, matter can also be identified based on its molecular structure and composition. This can be done using techniques such as X-ray diffraction, spectroscopy, and microscopy, which allow scientists to examine the atomic and molecular structure of matter.

Finally, the chemical formula of a substance can also be used to identify it. The chemical formula specifies the types and numbers of atoms present in the substance, which can be used to determine its chemical properties and behavior.

If there is a non-trivial linear combination of the vectors that equals 0, then a set of vectors is said to be linearly dependent.

Physical quantities can be represented using vectors. Vectors are most frequently employed in physics to describe displacement, velocity, and acceleration. Vectors are depicted as arrows and combine magnitude and direction.

Because they may visually depict position, displacement, velocity, and acceleration, vectors are useful. It is crucial to indicate where the scale is being drawn at when drawing.

|v| =(x2 + y2) is the formula to calculate the magnitude of a vector in two dimensions, where v = (x, y). The equation |V| = (x2 + y2 + z2) can be used to calculate the magnitude of a vector in three dimensions, where V = (x, y, z).

Therefore, vectors because you frequently do not have enough room to draw them at the scale they represent.

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The light year is an unit of measure for distance. It is defined as the distance travelled by light in a vacuum over the course of a year.

A vacuum is a space area that is either devoid of matter or has a pressure so minimal that any particles there have no bearing on any processes occurring there. It is a condition that has a pressure that is measured in units of pressure and is much lower than the mean air pressure.

The quantity of force applied to a certain region is referred to as pressure. So either a strong force or a strong force applied over a short area can cause a lot of pressure (or do both).

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A stopped roller coaster cart (velocity = 0 m/s) with a mass of 12,000 kg starts from the top of

the track at a height of 35 meters. It begins to roll down to the bottom (where height will be 0 meters).

KE = PE = mgh

KE = (12,000)(9.8)(35)

= 4,116,000

What is height?

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The force in the cord ab is 37.6 lb when being lifted at a constant speed, and the angle u for balance.

The rotation of the earth is an example of a body that is moving with uniform velocity when its speed is increasing throughout an interval of time.

The sum of the forces in each direction must be zero in order to lift the block at a steady speed.

XFx = 0 : F sin θ − T sin 20° = 0

XFy = 0 : T cos 20° − F cos θ − 20 = 0

The tension in cord CAD stays constant throughout because there is no friction on the pulley: F = 20 lb.

20 sin θ − T sin 20° = 0......... (1)

T cos 20° − 20 cos θ − 20 = 0 ........(2)

Solve equation (1) for T

T = 20 sin θ/sin 20

and substitute it into equation (2).

(20 sin θ/sin 20°)cos 20° − 20 cos θ − 20 = 0

cot 20°sin θ − cos θ − 1 = 0

cot 20°sin θ − 1 = cos θ

cot 20°sin θ − 1 = √1 − sin2θ

cot²20°sin²θ − 2 cot 20°sin θ + 1 = 1 − sin²θ

(cot²20° + 1) sin²θ − 2 cot 20°sin θ = 0

csc²20°sin²θ − 2 cot 20°sin θ = 0

(csc²20°sin θ − 2 cot 20°) sin θ = 0

csc²20°sin θ − 2 cot 20° = 0 or sin θ = 0

sin θ = 2 cot 20°/csc² 20°

= 2 cos 20°sin 20° = sin 40° or sin θ = 0

θ = 40° or θ ≠ 0°.

Substitute this nonzero value for θ into the formula for T.

T =20 sin θ/sin 20°

≈ 37.6 lb

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The secant modulus and the tangent modulus for the stress level of 50,000 psi are both 4.5x10-9 psi-1.

Secant modulus is a measure of a material's ability to resist deformation under stress. It is the ratio of stress to strain in a material and is equal to the slope of a line drawn between two points on a stress-strain curve.

The secant modulus is the slope of the line connecting two points on the stress-strain curve. In this case, the two points we need to consider are (50,000 psi, ε) and (0 psi, 0).
Therefore, the secant modulus is given by:
secant modulus = (ε - 0) / (50,000 psi - 0 psi)
Plugging in the equation for ε, we get:
secant modulus = (0.3x10-16x50,0003 - 0) / (50,000 psi - 0 psi)
secant modulus = 4.5x10-9 psi-1
The tangent modulus is the slope of the tangent line to the stress-strain curve at a given point. In this case, the point is (50,000 psi, ε).
Therefore, the tangent modulus is given by:
tangent modulus = dε/dσ
Plugging in the equation for ε, we get:
tangent modulus = (3x10-16x50,0002) / (1 psi)
tangent modulus = 4.5x10-9 psi-1
Therefore, the secant modulus and the tangent modulus for the stress level of 50,000 psi are both 4.5x10-9 psi-1.

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After applying the gravitational potential energy, the amount work done in lifting a 35 kg sandbag to a height of 4.5 m would be 1,544 Joule

Gravitational potential energy is another name for work done against gravity. Because of this, if a mass (m) object is lifted through a height (h), the work done on it will be [m × g × h], and this energy will be stored as gravitational potential energy in the body.

Thus, the amount work done would be:

Work = m × g × h

         = 35 kg × 9.8 m/s² × 4.5 m

         = 1,543.5 Nm

         = 1,543.5 Joule

         = 1,544 Joule

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The pressure of the gas is 0.970 atm.

The pressure of a gas can be calculated using the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

First, we need to find the number of moles of N2, which can be calculated using the molar mass of N2 and the mass of N2 in the container:

n = m/M

n = 0.293g / 28.02 g/mol

n = 0.0104 mol

Next, we need to find the temperature in Kelvin, which can be calculated using the root-mean-square speed of the gas molecules:

T = (2 * k * m / (3 * R))

T = (2 * 1.38 x 10^-23 J/K * 6.63 x 10^-27 kg * (178 m/s)^2 / (3 * 8.31 J/mol/K))

T = 298.15 K

Finally, we can use the ideal gas law to find the pressure:

P = nRT / V

P = (0.0104 mol * 8.31 J/mol/K * 298.15 K) / (1.62 L)

P = 0.970 atm

So the pressure of the gas is 0.970 atm.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

If we add a new residence in the circuit in parallel to the bulb of same resistance, the resultant resistance will get half the value of initial resistance [ when only bulb was connected in the circuit ], the current will increase as resultant resistance is half the original. and same current will flow in both the parallel wires.

So, by above information :

A.) Current would increase ? [ Yes ], As by ohms law, V = IR

and, if R is halfed, to maintain the same potential difference, current in the circuit will increase.

B.) Total voltage will decrease ? [ No ]... voltage will remain constant

C.) The current would stay the same ? [ yes ], it would increase...

D.) Total resistance would remain same ? [ No ], it will decrease...

The diffusion coefficient based on the provided data is 3.651 x 10^(-5) cm^2/s. (Option C)

The diffusion coefficient refers to the ratio of flux density to the negative of the concentration gradient in direction of diffusion. The diffusion coefficient in solids at different temperatures is generally found to be well predicted by the Arrhenius equation:

D=Do exp (-E/RT)

Where D is the diffusion coefficient (in m2/s), Do is the maximal diffusion coefficient (at infinite temperature; in m2/s), E is the activation energy for diffusion (in J/mol), T is the absolute temperature (in K), and R ≈ 8.31446 J/(mol⋅K) is the universal gas constant.

In the given case,

Do = 0.0047 cm/s = 4.7 x 10^-5 m/s

E = 18300 cal/mol = 76567.2 J/mol

T = 700°C = 973.15 K

Hence,

D=(4.7 x 10^(-5)) exp (-76567.2/(8.31446*973.15))

D=(4.7 x 10^(-5)) exp (-9.463)

D=3.651 x 10^(-9) m^2/s or 3.651 x 10^(-5) cm^2/s

Note: The question is incomplete.  The complete question probably is: What is the diffusion coefficient (D) for iron at 700°C, with an activation energy (E) of 18,300 cal/mol, and Do = 0.0047cm/s. A) 2.43E3 cm2/s B) 9.08E-9 cm2/s C) 3.64E-5 cm2/s D) 60.66 cm2/s.

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A and D are correct. A home run is the only type of successful hit, so the probabilities of each must be equal.

Additionally, a home run by definition is a successful hit, so the probability that he gets a successful hit must be greater than, or at least equal to, the probability that he hits a home run. B, C and E are incorrect since these probabilities can be calculated and it is possible to say which one is greater.

The probability is a measure of how likely an event is to occur. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of potential outcomes. For example, if the probability of flipping a coin and getting heads is 0.5, it means that there is a 50% chance of getting heads when flipping the coin.

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As the object is raised, the gravitational potential energy of the system grows. When you drop something, the potential energy of the object is transformed into kinetic energy, which is the energy of the moving object, when it strikes the ground.

What is kinetic and potential energy?

Potential energy is the energy stored in an object or system due to its position or arrangement of elements. It is unaffected by the environment outside the installation or system, such as air or altitude. Conversely, kinetic energy refers to the energy of moving particles in a system or object.

An object's kinetic energy, unlike potential energy, relates to other stationary and moving objects in its immediate vicinity. Thus, the lifted object is in kinetic motion when released.

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The correct answer is (a): satellite 1's acceleration is half as much as satellite 2's.

This is due to the fact that the acceleration of two satellites in a circular orbit depends on their masses and orbital periods. Satellite 2 accelerates more quickly because it has twice as much mass as satellite 1. As a result, satellite 1 accelerates at a rate that is half that of satellite 2.

This results in a divergence in the orbits of the two spacecraft since satellite 1's speed will rise more slowly than satellite 2's. Over time, this difference will become more obvious, with satellite 1's orbit straying from a circular form more so than satellite 2's.

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Answer:

The gravitational force on the moon is approximately 1/6th of the gravitational force on Earth. This means that the value of gravity on the moon is 1.62 m/s2.

Answer:

on earth the value of gravity on moon is 1.625 m/s2

Explanation:

1.625 m/s2

The magnitude of your total displacement is 745 m.

The total displacement of the your motion is calculated by applying the following formula as shown below;

Δx = x₂ - x₁

where;

The magnitude of your total displacement is calculated as follows;

Δx = ( 23 m/s x 155 s ) - ( 12 m/s x 235 s )

Δx = 745 m

Thus, the magnitude of your total displacement is based on the change of your position.

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