a ball of diameter 10 cm and mass 10 grams is dropped in a container of water. the cross sectional area of the container is 100 cm2.. what is the change in the height of the water column

Answers

Answer 1

Answer:

h = 9.83 cm

Explanation:

Let's analyze this interesting exercise a bit, let's start by comparing the density of the ball with that of water

       

let's reduce the magnitudes to the SI system

         r = 10 cm = 0.10 m

         m = 10 g = 0.010 kg

         A = 100 cm² = 0.01 m²

the definition of density is

          ρ = m / V

the volume of a sphere

         V = [tex]\frac{4}{3} \ \pi r^{3}[/tex]

          V = [tex]\frac{4}{3}[/tex] π 0.1³

          V = 4.189 10⁻³ m³

let's calculate the density of the ball

           ρ = [tex]\frac{0.010}{4.189 \ 10^{-3} }[/tex]

           ρ = 2.387 kg / m³

the tabulated density of water is

         ρ_water = 997 kg / m³

we can see that the density of the body is less than the density of water. Consequently the body floats in the water, therefore the water level that rises corresponds to the submerged part of the body. Let's write the equilibrium equation

            B - W = 0

            B = W

             

where B is the thrust that is given by Archimedes' principle

           ρ_liquid  g V_submerged = m g

           V_submerged = m / ρ_liquid

we calculate

            V _submerged = 0.10 9.8 / 997

             V_submerged = 9.83 10⁻⁴ m³

The volume increassed of the water container

           V = A h

            h = V / A

let's calculate

            h = 9.83 10⁻⁴ / 0.01

            h = 0.0983  m

this is equal to h = 9.83 cm


Related Questions

14. After finishing her homework, Sue climbs up a 5.00 m high flight of stairs to her bedroom
Find the magnitude of Sue's weight
and how much
work Sue does in climbing the stairs if she
has a mass of 50.0 kg? (4.90 x 2 N, 2450J)

Answers

Explanation:

Given parameters:

Height  = 5m

Mass of Sue  = 50kg

Unknown:

Magnitude of Sue's weight  = ?

Work done by Sue = ?

Solution:

Weight is the vertical force exerted by a body in the presence of gravity.

Mathematically;

        W = mg

m is the mass

g is the acceleration due to gravity  = 9.8m/s²

  Weight  = 50 x 9.8  = 490N

Work done  = Force x distance = weight x height

 Work done  = 490 x 5 = 2450J

which of the following is not a mechanical form of energy?
a. Nuclear
b. Kinetic
c. Spring potential
d. Gravitational potential ​

Answers

Answer:

The answer is Spring Potential

Explanation:

Because all the others are a mechanical form of energy

Help! Help!

___ are a primary way to discourage drinking and driving.
A. High prices for alcohol
B. Scare tactics
C. Laws

Answers

Answer:

Laws

Explanation:

Laws are a primary way discourage drinking and driving

A primary way to discourage drinking and driving is Law.

What is drinking and driving?

The person who takes in alcohol and then drives on the road. This is strictly prohibited.

Laws against the  'drinking and driving' will make people get scared of getting charged or sentenced to jail for some years. Lot of accidents have caused when there were no laws against the action.

Thus, Laws are a primary way to discourage drinking and driving.

Learn more about drinking and driving.

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Two identical plastic cups contain the same amount of water at two different temperatures, as shown to the left. Both cups are placed in a room at 25° Celsius. At the time cups were placed in the room, in which cup do the water molecules have higher average kinetic energy? ( Cup 1 © Cup 2​

Answers

Answer:

the molecules will begin to move slowly and will turn to ice

Explanation:

hope this was good or not not sure if am right but yeah

let's say you hypothetically ran over someone with your car, and they are now under your car in between the front wheels and the back wheels, right, and they're stuck as in can't breathe type stuck, right, do you keep driving so they can breathe or do you let them chill under your car?
just curious...​

Answers

question: is this actually hypothetical?

Explanation:

also just leave the car there go get some McDonald's or sum and come back and if they're still breathing then go ahead and move the car .

Answer:

the same thing the last guy said

A(n) 636 kg elevator starts from rest. It moves upward for 4.5 s with a constant acceleration until it reaches its cruising speed of 2.05 m/s. The acceleration of gravity is 9.8 m/s 2 . Find the average power delivered by the elevator motor during this period. Answer in units of kW.

Answers

Answer:

The average power delivered by the elevator motor during this period is 6.686 kW.

Explanation:

Given;

mass of the elevator, m = 636 kg

initial speed of the elevator, u = 0

time of motion, t = 4.5 s

final speed of the elevator, v = 2.05 m/s

The upward force of the elevator is calculated as;

F = m(a + g)

where;

m is mass of the elevator

a is the constant acceleration of the elevator

g is acceleration due to gravity = 9.8 m/s²

[tex]a = \frac{v-u}{t} \\\\a = \frac{2.05 -0}{4.5} \\\\a = 0.456 \ m/s^2[/tex]

F = (636)(0.456 + 9.8)

F = (636)(10.256)

F = 6522.816 N

The average power delivered by the elevator is calculated as;

[tex]P_{avg} = \frac{1}{2} (Fv)\\\\P_{avg} = \frac{1}{2} (6522.816 \ \times \ 2.05)\\\\P_{avg} = 6685.89 \ W\\\\P_{avg} = 6.68589 \ kW\\\\P_{avg} = 6.686 \ k W[/tex]

Therefore, the average power delivered by the elevator motor during this period is 6.686 kW.


Define friction. Prove that tangent of angle of friction is equal to coefficient
of friction.​

Answers

Answer:

Friction is the force that opposes movement between moving objects.

The angle at which one object starts to slip on the other is directly related to the coefficient. When the two objects are horizontal there is no frictional force. So, the coefficient of static friction is equal to the tangent of the angle at which the objects slide. A similar method can be used to measure μk.

Explanation:

Answer:

brainliest plsssssss

Explanation:

The resistance that one surface or object encounters when moving over another

What happens to most of the light waves that strike a clear pane of glass? O A. absorption B. diffraction O C. reflection O D. transmission​

Answers

slight reflect but most goes through because glass is transparent

Most of the light waves that strike a clear pane of glass reflects. Details about reflection can be found below.

What is reflection?

Refection in physics is the property of a propagated wave being thrown back from a surface such as a mirror.

Mirror is an example of an object that could be hit by an incumbent wave, however, most of the light waves that hit the mirror surface gets reflected back.

Therefore, most of the light waves that strike a clear pane of glass reflects.

Learn more about refection at: https://brainly.com/question/15487308

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An automobile which set the world record for acceleration increase speed from rest to 96 km/h in 3.07 seconds what distance traveled by the time the final speed was achieved

Answers

Answer:

41.02m

Explanation:

Given parameters:

Initial velocity = 0m/s

Final velocity  = 96km/hr

Time taken  = 3.07s

Unknown:

Distance traveled by the time the final speed was achieved = ?

Solution:

To solve this problem, we first find the acceleration of the car;

     Acceleration  = [tex]\frac{v - u }{t}[/tex]

v is the final velocity

u is the initial velocity

t is the time taken

  Now convert the the final velocity to m/s;

          96km/hr to m/s;

               1 km/hr  = 0.278m/s

               96km/hr  = 96 x 0.278 = 26.7m/s

Now;

 Acceleration  = [tex]\frac{26.7 - 0}{3.07}[/tex]   = 8.69m/s²

So;

   v²  = u²  + 2as

v is the final velocity

u is the initial velocity

a is the acceleration

s is the distance

             26.7²  = 0²  + 2 x 8.69 x s

             712.89  = 17.38s

                  s  = 41.02m

The least count of stopwatch is 0.2s.The time of 20 oscillations of a pendulum was measured to be 25s.Find the percentage error in the measurement of time​

Answers

Answer:

0.8%

Explanation:

We are given;

Number of oscillations; n = 20

Time taken; t = 25 s

Formula for period of oscillation;

T = t/n = 25/20 = 1.25 s

We are told that the least count is 0.2 s. Thus, error is; ΔT = 0.2 s

percentage error in the measurement of time is given by;

(0.2/(20 × 1.25)) × 100% = 0.8%

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