Asteroid X orbits moon XYZ with a speed of 500m/s and a centripetal force of 1500N. Asteroid X, Y and Z all have the same mass. If asteroid Y orbits moon XYZ with the same orbital radius as asteroid X but at a speed of 100m/s. What is the centripetal force acting acting on asteroid Y? If asteroid Z orbits moon XYZ with a speed of 1500m/s but on orbital radius that is half of asteroid X, what is the centripetal force acting asteroid Z? ​

Answer:

(A) The speed just as it left the ground is 30.25 m/s

(B) The maximum height of the rock is 46.69 m

Explanation:

Given;

weight of rock, w = mg  = 20 N

speed of the rock at 14.8 m, u = 25 m/s

(a) Apply work energy theorem to find its speed just as it left the ground

work = Δ kinetic energy

F x d = ¹/₂mv² - ¹/₂mu²

mg x d = ¹/₂m(v² - u²)

g x d = ¹/₂(v² - u²)

gd = ¹/₂(v² - u²)

2gd = v² - u²

v² = 2gd  + u²

v² = 2(9.8)(14.8) + (25)²

v² = 915.05

v = √915.05

v = 30.25 m/s

B) Use the work-energy theorem to find its maximum height

the initial velocity of the rock = 30.25 m/s

at maximum height, the final velocity = 0

- mg x H = ¹/₂mv² - ¹/₂mu²

- mg x H = ¹/₂m(0) - ¹/₂mu²

- mg x H = - ¹/₂mu²

2g x H = u²

H = u² / 2g

H = (30.25)² / 2(9.8)

H = 46.69 m

Answer:

the work done by the steam during this process = 119.575 kJ

Explanation:

From the information given:

At state 1

Let obtain the specific volume of the saturated vapor from the Saturated water- Pressure table A-5 at the pressure of 100 kPa

[tex]v_1 = v_{g \ 100 \ kPa)[/tex]

[tex]v_1 = 1.6941 \ m^3 /kg[/tex]

where [tex]v_1[/tex] is the specific volume of the saturated vapor at state 1.

At state 2:

From the tables A-6 of Superheated water at the pressure of 100 kPa or 0.1 MPa and at the temperature of 200°C, the specific volume [tex]v_2 = 2.1724 \ m^3 /kg[/tex]

where [tex]v_2[/tex] is the specific volume of the superheated water at state 2.

The workdone by the steam during the process can be expressed by the formula:

[tex]W = P(V_2 -V_1)[/tex]

[tex]W = mP(v_2-v_1)[/tex]

where;

m = mass of the saturated water vapor

P = pressure of the saturated water vapor

[tex]V_2 =[/tex] volume of the superheated water at state 2

[tex]V_1 =[/tex] volume of the saturated water at state 1

Replacing our values ;

W = 2.5 (100) ( 2.1724 -1.6941)

W = 250(0.4783 )

W = 119.575 kPa.m³ [tex]\times \dfrac{1 \ kJ}{1 \ kPa.m^3}[/tex]

W = 119.575 kJ

∴

the work done by the steam during this process = 119.575 kJ

Answer:

5.2 centimicro meter or 5.2 cμm

Explanation:

Prefixes allow scientists report numbers logically depending on the order of the magnitude of the numbers. For example to represent 4 x 10⁻³m, it is more handy to say : 4 millimetre, where milli- is the prefix for 10⁻³.

Common prefixes are:

deci = 10⁻¹                     deca = 10¹                    

centi = 10⁻²                   hecto = 10²

milli  = 10⁻³                    kilo  = 10³                      

micro = 10⁻⁶                  mega = 10⁶

nano = 10⁻⁹                   giga = 10⁹

pico = 10⁻¹²                   terra = 10¹²

femto = 10⁻¹⁵                peta = 10¹⁵

Now, let's represent the given diameter: 5.2 x 10⁻⁸ m

Since the 10⁻⁸ prefix is not common (or maybe doesn't even exist), the way around this is to break it into bits such as:

10⁻⁸ = 10⁻² x 10⁻⁶           [10⁻² = centi,  10⁻⁶ = micro ]

10⁻⁸ = centimicro

Therefore, 5.2 x 10⁻⁸ m becomes 5.2 centimicro meter.

The symbol is 5.2 cμm

Where c = centi, μ = micro.

Answer:

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment.

Explanation:

Answer:

science is the knowledge gained through observations and experimentations

Characteristics

consistency

observability

predictability

testability

tentativeness

components of nature are soil,atmosphere and radiation

Answer:

7 valence electrons is right answer

Explanation:

2 elections in first shell and 5 electrons in second shell which total makes seven electrons.

hope it helped you:)

Explanation:

It is given that,

Wavelength of x-rays = 2 nm

Plane spacing, d = 0.281 nm

It is assumed to find the scattering angle for second order maxima.

For 2nd order, Bragg's law is given by :

[tex]2d\sin\theta=n\lambda[/tex]

For second order, n = 2

[tex]\sin\theta=\dfrac{n\lambda}{2d}\\\\\sin\theta=\dfrac{2\times 2\ nm}{2\times 0.28\ nm}\\\\\theta=\sin^{-1}(7.14)[/tex]

Here, θ is not defined. Also, the wavelength of x-rays is more than the plane spacing. It means that it cannot produce any diffraction maximum.

Answer:

Explanation:

For constructive interference of two coherent light waves at a point , the condition is as follows

path difference = n x wavelength where n is any integer like  1 , 2 , 3 ,  .... etc .

Given in the question , path difference of light from the two sources

= 355 - 141 = 214 m

So applying the formula above ,

214 = n x wavelength

wavelength = 214 / n

For largest value of wavelength , n should be smallest . The smallest value of n is 1 .

so ,

largest wavelength possible for constructive interference

= 214 / 1

= 214 m .

Answer:

the nucleus-containing central part of a neuron exclusive of its axons and dendrites that is the major structural element of the gray matter of the brain and spinal cord, the ganglia, and the retina. — called also perikaryon, soma.

Answer:

Your body cells use the oxygen you breathe to get energy from the food you eat. This process is called cellular respiration. During cellular respiration the cell uses oxygen to break down sugar. The opposite takes place in the cells where the blood releases oxygen and picks up carbon dioxide.

"Should wolves be reintroduced into national parks" is a question that cannot be answered through making measurements, therefore the correct answer is option C.

A unit of measurement is a specified magnitude of a quantity that is established and used as a standard for measuring other quantities of the same kind. It is determined by convention or regulation. Any additional quantity of that type can be stated as a multiple of the measurement unit.

A length, for instance, is a physical quantity. A defined, predetermined length is represented by the length unit known as the meter.

A qualitative type of question cannot be answered while making a quantitative measurement.

Thus, the question of whether wolves should be reintroduced into national parks cannot be answered by taking measurements, so option C is the appropriate response.

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Answer:

The answer is below

Explanation:

a) The location ӯ of the center of mass G of the pendulum is given as:

[tex]y=\frac{0+(\pi*(0.3\ m) ^2*12kg/m^2*1.8\ m-\pi*(0.1\ m) ^2*12kg/m^2*1.8\ m)+0.75\ m*1.5\ m *3\ kg/m}{(\pi*(0.3\ m) ^2*12kg/m^2-\pi*(0.1\ m) ^2*12kg/m^2)+3\ kg/m^2*0.8\ m+3\ kg/m^2*1.5\ m} \\\\y=0.88\ m[/tex]

b)  the mass moment of inertia about z axis passing the rotation center O is:

[tex]I_G=\frac{1}{12}*3(0.8)(0.8)^2+ 3(0.8)(0.888)^2-\frac{1}{2}*(12)(\pi)(0.1)^2(0.1)^2 -(12)(\pi)(0.1)^2(1.8-\\0.888)^2+\frac{1}{2}*(12)(\pi)(0.3)^2(0.3)^2 +(12)(\pi)(0.3)^2(1.8-0.888)^2+\frac{1}{12}*3(1.5)(1.5)^2+\\3(1.5)(0.888-0.75)^2\\\\I_G=13.4\ kgm^2[/tex]

c) The mass moment of inertia about z axis passing the rotation center O is:

[tex]I_o=\frac{1}{12}*3(0.8)(0.8)^2+ \frac{1}{3}* 3(1.5)(1.5)^2+\frac{1}{2}*(12)(\pi)(0.3)^2(0.3)^2 +(12)(\pi)(0.3)^2(1.8)^2-\\\frac{1}{2}*(12)(\pi)(0.1)^2(0.1)^2 -(12)(\pi)(0.1)^2(1.8)^2\\\\I_o=13.4\ kgm^2[/tex]

Answer:

Therefore, the situation in which both the instantaneous velocity and acceleration become zero, is the situation when the ball reaches the highest point of its motion.

Explanation:

When a ball is thrown upward under the free fall action of gravity, it starts to loose its Kinetic Energy as it moves upward. As the ball moves in upward direction, its kinetic energy gradually converts into its potential energy. As a result the speed of the ball starts to decrease as it moves up. Therefore, at the highest point during its motion, the velocity of ball becomes zero and it stops at the highest point for a moment, and then it starts to fall back down, under the influence of gravitational force.

Therefore, the situation in which both the instantaneous velocity and acceleration become zero, is the situation when the ball reaches the highest point of its motion.

Answer:

[tex]I=0.0795\ W/m^2[/tex]

Explanation:

Given that,

Power of electromagnetic energy, P = 100 W

We need to find the intensity at a distance of 10 m from the source. Intensity is equal to the power per unit area. So,

[tex]I=\dfrac{P}{4\pi r^2}\\\\I=\dfrac{100}{4\pi (10)^2}\\\\I=0.0795\ W/m^2[/tex]

So, the intensity at a distance of 10 m is [tex]0.0795\ W/m^2[/tex]

Answer:

The correct one is that the force on B is half of the force on A

Explanation:

Because radius for the inside of the curve is half the radius for the outside and Car A travels on the inside while car B, travels at equal speed on the outside of the curve. Thus force on B will be half on A

Answer:

m = 312.5

Explanation:

Given that,

The focal length of the objecive lens, [tex]f_o=1\ cm[/tex]

The focal length of eye piece, [tex]f_e=2\ cm[/tex]

length of the tube, L = 25 cm

We need to find the magnitude of the overall magnification of the microscope. It is given by the formula as follows :

[tex]m=\dfrac{L}{f_o}\times \dfrac{D}{f_e}[/tex]

D = 25 cm

So,

[tex]m=\dfrac{25}{1}\times \dfrac{25}{2}\\\\m=312.5[/tex]

So, the overall magnification of the microscope is 312.5.

Answer:

175 N/m

Explanation:

Given:

Force = F=  14.0 N

Distance = x = 8.00 cm = 0.08 m

To find:

spring constant

Solution:

spring constant is calculated by using Hooke's law:

k =  F/x

Putting the values in above formula:

k = 14.0 / 0.08

k = 175 N/m

Answer:

1.9×10⁻⁵ °C⁻¹

Explanation:

Coefficient of linear expansion: This can be defined as as increase in length of a material, per unit length per degree rise in temperature, The S.I unit is (K⁻¹).

From the question above,

α = ΔL/L(T₂-T₁)................... Equation 1

Where α = coefficient of linear expansion, ΔL = Change in length, L = original length, T₁ = Initial Temperature, T₂ = Final temperature.

Given: ΔL = 1.4 cm = 0.014 m, L = 24.5 m, T₁ = 4.00°C, T₂ = 34°C

Substitute these values into equation 1

α = 0.014/[24.5(34-4)]

α = 0.014/735

α = 1.9×10⁻⁵ °C⁻¹

Answer:

Average speed = 2.22m/s

Velocity = 0.89 m/s west

Explanation:

(i) Since speed is a scalar quantity, the direction of movement by the person is irrelevant. Therefore,

Average speed = total distance traveled / time taken

Where;

Total distance = 70m + 30m = 100m

Time taken = 45 seconds

Average speed = 100 / 45 = 2.22m/s

(ii) However, velocity is a vector quantity and so the direction of movement by the person is of utmost importance. Therefore,

Velocity = displacement / time taken

Where;

displacement = -70m + 30m    [West direction is taken as negative and east is taken as positive]

displacement = -40m     [The negative sign just means that the net displacement is in the direction of the West].

Thus, displacement can be written as 40m west.

Therefore,

Velocity = 40 / 45 = 0.89m/s west

Answer:

The critical angle is 34 degree.

Explanation:

Given the index refraction = 1.77

We have to find the critical angle of sapphire when the air has the index of refraction of 1.0.

Use the below formula to find the angle.

sin(θ)c = 1 / n

sin(θ) c  = 1 / 1.77

(θ) c  = Sin^-1 (0.565)

= 34.4 degree

= 34 degrees.

Thus, the critical angle is 34 degree.

Answer:

A. a meteor traveling unhindered through space

Explanation:

Answer:

A

Explanation:

Ansthe answer is A

Explanation:

It is constructed in such a way that possible answers can be

tested.

Answer:

F' = (3/2)F

Explanation:

the formula for the electric field strength is given as follows:

E = F/q

where,

E = Electric Field Strength

F = Force due to the electric field

q = magnitude of charge experiencing the force

Therefore,

F = E q   ---------------- equation (1)

Now, if we half the electric field strength and make the magnitude of charge triple its initial value. Then the force will become:

F' = (E/2)(3 q)

F' = (3/2)(E q)

using equation (1)

F' = (3/2)F

When the charge of the particle is tripled, and magnetic field strength is halved, the force increases by factor of 1.5 (1.5 F)

The force experienced by a particle placed in magnetic field is given as;

F = qvB

where;

When the charge of the particle is tripled, q₂ = 3q and magnetic field strength is halved, B₂ = 0.5B.

The magnetic force of the particle is determined as;

[tex]F = qvB\\\\ v = \frac{F}{qB} \\\\ \frac{F_1}{q_1B}_1 = \frac{F_2}{q_2B_2}\\\\ F_2 = \frac{F_1 q_2B_2}{q_1 B_1} \\\\ F_2 = \frac{F \times 3q_1\times 0.5B_1}{q_1B_1} \\\\ F_2 = 1.5 F[/tex]

Thus, when the charge of the particle is tripled, and magnetic field strength is halved, the force increases by factor of 1.5 (1.5 F).

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All known species are made up of small structures called cells, according to observations obtained using a microscope; this theory is supported by empirical data..Option A is corect.

An investigation is defined as a thorough search or inspection. The investigative process is a series of tasks or procedures that include obtaining evidence, analyzing the material, and developing and validating theories.

Respectfully recognize any information or points of view that contradict your contention. You have to demonstrate to the reader in the refutation why your position is superior to the opposing notion.

Observations made using microscopes reveal that all known organisms are composed of tiny structures called cells the explanation is based on scientific evidence.

Hence option A is corect.

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Answer:

1.14*10^-3m

Explanation:

We know that

Volume= mass/ density

But

Area x depth= mass/density

πr²*depth= mass/density

r²=m/πdp

So

r= √0.35/3.142*0.085*1000

r= 1.14*10^-3m

Answer:

AFter 3.5 s, the wagon is moving at:   [tex]4.62\,\,\frac{m}{s}[/tex]

Explanation:

Let's start by finding first the net force on the wagon, and from there the wagon's acceleration (using Newton's 2nd Law):

Net force = 250 N + 178 N = 428 N

Therefore, the acceleration from Newton's 2nd Law is:

[tex]F=m\,*\,a\\a = \frac{F}{m} \\a= \frac{428}{325}\, \frac{m}{s^2} \\a\approx 1.32 \,\,\frac{m}{s^2}[/tex]

So now we apply this acceleration to the kinematic expression for velocity in an object moving under constant acceleration:

[tex]v_f=v_i+a\,*\,t\\v_f=0+1.32\,*\,3.5\,\,\frac{m}{s} \\v_f=4.62\,\,\frac{m}{s}[/tex]

Answer:

No, the pendulum's period of oscillation does not depend on initial angular displacement.

Explanation:

Given that,

For small angle, the pendulum's period of oscillation depend on initial angular displacement from equilibrium.

We know that,

The time period of pendulum is defined as

[tex]T=2\pi\sqrt{\dfrac{l}{g}}[/tex]

Where, l = length of pendulum

g = acceleration due to gravity

So, The time period of pendulum depends on the length of pendulum and acceleration due to gravity.

It does not depend on the initial angular displacement.

Hence, No, the pendulum's period of oscillation does not depend on initial angular displacement.

Answer:

Difference in height = 7.5 cm

Explanation:

We are given;.

Height of ethyl alcohol;h2 = 20 cm = 0.2 m

Density of glycerin: ρ1 = 1260 kg/m³

Density of ethyl alcohol; ρ2 = 790 kg/m³

To get the difference in height, the pressure at the top of the open end must be equal to the pressure at the point where the liquids do not mix since both points will be at different levels after the pouring.

Thus;

P1 = P2

Formula for pressure is; P = ρgh

Thus;

ρ1 × g × h1 = ρ2 × g × h2

g will cancel out to give;

ρ1 × h1 = ρ2× h2

Making h1 the subject, we have;

h1 = (ρ2× h2)/ρ1

h1 = (790 × 0.2)/1260

h1 = 0.125 m

Difference in height will be;

Δh = h2 - h1

Δh = 0.2 - 0.125

Δh = 0.075 m = 7.5 cm

The difference in height between the top surface of the glycerin and the top surface of the alcohol as per Pascal's law is 7.5 cm.

As per Pascal's law, "The pressure at any point of the vessel filled with incompressible liquid is same".

Given data -

The height of both section is, h2 = 20 cm = 0.20 m.

The density of glycerine is, [tex]\rho_{1} = 1260 \;\rm kg/m^{3}[/tex].

The density of alcohol is, [tex]\rho_{2} = 790 \;\rm kg/m^{3}[/tex].

The pressure at the top of the open end must be equal to the pressure at the point where the liquids do not mix since both points will be at different levels after the pouring. Therefore,

P1 = P2

The formula for pressure is;

P = ρgh

Thus;

ρ1 × g × h1 = ρ2 × g × h2

ρ1 × h1 = ρ2× h2

h1 = (ρ2× h2)/ρ1

h1 = (790 × 0.2)/1260

h1 = 0.125 m

Difference in height will be;

Δh = h2 - h1

Δh = 0.2 - 0.125

Δh = 0.075 m

Δh = 7.5 cm

Thus, we can conclude that the difference in height between the top surface of the glycerin and the top surface of the alcohol is 7.5 cm.

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(1) -2.0025m/s.

(2) It moves west.

(3) 3.3375m/s.

(4) It moves east.

Assuming the collision occurred in an isolated system. This means that total momentum of the system of pucks is conserved. Since no external forces are acting on these pucks, the momentum of the pucks before collision is equal to the momentum of the pucks after collision. i.e

(p₁)₀ + (p₂)₀ = (p₁)₁ + (p₂)₁              -------------(i)

Where;

(p₁)₀ = momentum of the 0.45kg puck before collision

(p₂)₀ = momentum of the 0.990kg puck before collision

(p₁)₁ = momentum of the 0.45kg puck after collision

(p₂)₁ = momentum of the 0.990kg puck after collision

But;

(p₁)₀ = m₁ u₁  

[m₁ = mass of the 0.45kg, u₁ = speed of the 0.45kg before collision]

(p₂)₀ = m₂u₂

[m₂ = mass of the 0.990kg, u₂ = speed of the 0.990kg before collision]

(p₁)₁ = m₁v₁

[m₁ = mass of the 0.45kg, v₁ = speed of the 0.45kg after collision]

(p₂)₁ = m₂v₂

[m₂ = mass of the 0.990kg, v₂ = speed of the 0.990kg after collision]

Equation (i) then becomes;

m₁ u₁ + m₂u₂ = m₁v₁ + m₂v₂    ----------------(ii)

From the question:

m₁ = 0.450kg

u₁ = +5.34m/s   [Taking east direction as positive]

m₂ = 0.990kg

u₂ = 0m/s    [since the second puck is initially at rest]

Substitute these values into equation (ii)

(0.450 x 5.34) + (0.990 x 0) = 0.45 v₁ + 0.990 v₂

2.403 + 0 = 0.45 v₁ + 0.990 v₂

2.403 = 0.45 v₁ + 0.990 v₂           ------------------(iii)

Also, since the collision is perfectly elastic, it means that the kinetic energy is conserved. i.e the total kinetic energy before collision is equal to the total kinetic energy after collision.

=> [tex]\frac{1}{2}[/tex]m₁ u²₁ + [tex]\frac{1}{2}[/tex]m₂u²₂ = [tex]\frac{1}{2}[/tex]m₁v²₁ + [tex]\frac{1}{2}[/tex]m₂v²₂

Substitute the necessary values into the above equation:

[[tex]\frac{1}{2}[/tex] x 0.45 x 5.34²] + [0] = [[tex]\frac{1}{2}[/tex] x 0.45 x v²₁] + [[tex]\frac{1}{2}[/tex] x 0.990 x v²₂]

[6.41601] = [0.225 x v²₁] + [0.495 x v²₂]  ------------------(iv)

Now let's solve equations (iii) and (iv) simultaneously

2.403 = 0.45 v₁ + 0.990 v₂

6.41601 = 0.225 x v²₁ + 0.495 x v²₂

let

v₁ = x

v₂ = y

2.403 = 0.45 x + 0.990 y                  ------------(5)

6.41601 = 0.225 x² + 0.495 y²         -------------(6)

From equation (5), make x subject of the formula

2.403 = 0.45x + 0.990y

0.45x = 2.403 - 0.990y         [divide through by 0.45]

x = 5.34 - 2.2y    ----------------(m)

Substitute x into equation (6)

6.41601 = 0.225 (5.34 - 2.2y)² + 0.495 y²     [expand bracket]

6.41601 = 0.225 [28.5156 - 23.496y + 4.84y²] + 0.495 y²   [remove bracket]

6.41601 = 6.41601 - 5.2866y + 1.089y² + 0.495 y²

1.584y² - 5.2866y = 0

y(1.584y - 5.2866) = 0

y = 0       or       1.584y - 5.2866 = 0

y = 0       or       1.584y = 5.2866

y = 0       or       y = 3.3375

Since y = v₂ cannot be zero because the puck will definitely move after collision, the second value of y = 3.3375 is considered.

Substitute this value into equation (m)

x = 5.34 - 2.2y

x = 5.34 - 2.2(3.3375)

x = 5.34 - 7.3425

x = -2.0025

Therefore,

x = v₁ = -2.0025m/s

y = v₂ = 3.3375m/s

(1) From the analyses above, the speed of the 0.450kg puck after collision is -2.0025m/s.

(2) Since the speed is negative, it shows that the 0.45kg puck moves opposite the direction at which it was moving before collision. It moves west.

(3) The speed of the 0.990kg puck after collision is 3.3375m/s.

(4) Since the speed is positive, it shows that the 0.990kg puck moves east. Remember that east has been taking as the positive direction.

Answer:

The  frequency is  [tex]f = 439.5 \ Hz[/tex]        

Explanation:

From the question we are told that

   The frequency of the  tuning fork is  [tex]f_t = 440 \ Hz[/tex]

   The beat period is  [tex]T = 2 \ s[/tex]

Generally the beat frequency is mathematically represented as

       [tex]f_b = \frac{1}{T}[/tex]

       [tex]f_b = \frac{1}{2}[/tex]

      [tex]f_b = 0.5 \ Hz[/tex]

The  beat frequency is also represented mathematically as

     [tex]f_b = f_t - f[/tex]

Where  [tex]f[/tex] is the frequency of the piano

 So

       [tex]f = 440 - 0.5[/tex]  

       [tex]f = 439.5 \ Hz[/tex]        

Answer:

m = 69.9 kg

Explanation:

The mass and the weight of an object are two different quantities. Mass is basically the amount of matter that is present in a body. It remains same everywhere in the universe and measured in kilograms.

Weight is basically a force. It is the force by which earth attracts everything towards itself. The weight of an object changes from planet to planet, with the change in value of the gravitational acceleration (g).

Therefore, the relation between mass and weight of an object is given by the following formula:

W = mg

m = W/g

where,

m = mass = ?

W = Weight = 685 N

g = 9.8 m/s²

Therefore,

m = (685 N)/(9.8 m/s²)

m = 69.9 kg

The mass of an object that experience a gravitational force of 685N near the earth is approximately 69.90 kg

The mass and weight are 2 different quantities.

The mass of a substance is the amount of matter present in it. Mass is measured in kilograms

The Weight is the measurement of gravitational pull of planet towards the object. Therefore, weight is a force and measured in Newton.

Mathematically, the weight can be express as follows

W = mg

where

m = mass

g = acceleration due to gravity = 9.8 m/s²

Therefore,

685 = 9.8 × m

m = 685 / 9.8

m = 69.8979591837

m = 69.90 kg

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