Answer:
Pressure
Explanation:
One of the theories propounded by the Kinetic molecular theory, and which also provides an explanation of the several gas laws, is the statement that the gas molecules in a container, travel in straight lines and are in constant collision with themselves and the walls of the container, thus exerting force. This force is the pressure which is defined as the force per unit area.
There is no loss of energy in the collisions involving the gas molecules and that is why their movement can be described as elastic. The descriptions of the behavior of gas molecules in the Kinetic Molecular Theory, give rise to Charles law, Boyle's Law, Avogadro's Laws, Dalton's Law, and Amonton's Law.
Answer:
The pressure
Explanation:
Molecules of gases are constantly in motion, colliding with the walls of their container. This constant collision impacts force on the walls of the container, which depends on the speed with which the molecules are moving. The speed with which these molecules travel depends on the average kinetic energy of the molecules, which is proportional to the temperature.
This force when exerted per unit area is the pressure the gases exert on the walls of the container.
What is the speed of a cheetah that travels 176.4 meters in 4.5 seconds?
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{39.2 \: m/ {s} \: }}}}[/tex]
Explanation:
Given,
Distance travelled ( d ) = 176.4 meters
Time taken ( t ) = 4.5 seconds
Finding the speed of a cheetah
Speed [tex] \sf{ = \frac{distance \: travelled}{time \: taken} }[/tex]
[tex] \sf{ = \frac{176.4}{4.5} }[/tex]
[tex] \sf{ = 39.2 \: m/ {s} \: }[/tex]
------------------------------------------------------------------------
Let's learn about Speed :
Suppose a body moves 20 m in 2 seconds, either on a curved path or on a straight path. So , 10 m is the distance travelled by the body in each second which can be written as 10 m/s. This is called speed of the body. Thus, Speed is defined as the distance travelled per unit time. It is the rate of distance travelled by a body.
Mathematically,
[tex] \boxed{ \bold{ \sf{speed = \frac{distance \: travelled}{time \: taken} }}}[/tex]
In SI system, the unit of distance is metre and time is second. Thus , the SI unit is speed is m/s.
Hope I helped!
Best regards!!
Can you solve this question please help me with this
Answer:
Explanation:
The velocity ratio of a wheel and axle is the ratio of the radius (R) of the wheel to the radius (r) of the axle. It is expressed as;
VR = R/r
Since radius = diameter/2
VR = (D/2)/(d/2)
VR = D/d
D is the diameter of the wheel and 'd' is the diameter of the axle.
Given VR = 3 and d = 5cm
3 = D/5
D = 15 cm
If the diameter of the wheel is 15cm, the radius of the wheel will be 15/2 = 7.5cm.
b) Workdone by the load = Load * distance moved by load
Given load = 60kg
Distance moved by load = 2π*radius of axle
Distance moved by load = 2π(0.025) = 0.157
workdone by load = 60* 0.157 = 9.42J
Effort = Workdone by load/distance moved by the wheel
Effort = 9.42/2π(0.075)
Effort = 9.42/0.471
Effort = 20kg
Hence the effort applied is 20kg
c) MA = Load/Effort
MA = 60/20
MA = 3
d) Efficiency = MA/VR * 100%
Efficiency = 3/3 * 100%
Efficiency = 100%
Determine the magnitude of the force that must be applied to a wooden block whose weight has a magnitude of 8N, so that it acquires an acceleration of 0.5 m / s²
Answer:
F = 0.408 N
Explanation:
It is given that,
Weight of a wooden block, W = 8 N
Weight, W = mg
m is mass of wooden block
[tex]m=\dfrac{W}{g}\\\\m=\dfrac{8\ N}{9.8\ m/s^2}\\\\m=0.816\ kg[/tex]
Acceleration of the block, a = 0.5 m/s²
Force, F = ma
[tex]F=0.816\ kg\times 0.5\ m/s^2\\\\F=0.408\ N[/tex]
So, the magnitude of force applied to the wooden block is 0.408 N.
A stone is dropped from the same height at Terai and at the top of the
mountain. Where does it fall faster? Why?
Answer:
It will fall at the same speed in both locations
Explanation:
When an object is falling, it is accelerated to the same degree irrespective of the height from which it is falling.
All objects on the earth's surface experience an acceleration due to gravity. This acceleration due to gravity is the same for all objects irrespective of their height or mass.
Hence for a stone dropped from the same height as Terai and the top of a mountain, the acceleration due to gravity is the same in both cases hence they will fall at the same speed.
State 1 difference between 1 way rotary motion and reversible rotary motion
Answer:
The difference between One-way as well as reversible rotary motion is described below.
Explanation:
Unless rotary motions occur restricted to single direction exclusively (i.e. whether clockwise as well as anti-clockwise only), it is defined as another rotary 'one-way' motion.This motor establishes that continuously variable movement at 360 ° chemically guided is conceivable. The rotating is regulated, and for a particular direction, the biochemical occurrences guiding rotation become incredibly selective.What is a substance?
A. a uniform mixture that can't be separated
В.a mixture that can be separated
С. a single component that can't be separated
D. a single component that can be separated
Answer:
С. a single component that can't be separated
Explanation:
Substance : It is the pure form of matter or we can say that it is a matter that contains only one type of molecule of atom. It can not be separated by physical process.
For example : Water is a substance.
Mixture : It is a combination of different type of atoms or molecules and it is an impure form.
For example : Sodium chloride with water is a mixture.
Hence, the correct option is, (C) a single component that can’t be separated.
A substance is a single component that can't be separated by the physical process therefore the correct answer is option C.
What is a Chemical compound?
A chemical compound is a mixture of two or more chemical components, whether they are related or unrelated.
For instance, the molecular H2O is composed of one hydrogen atom and two oxygen atoms.
For instance, water is a material that cannot be physically divided yet may be separated using electrolysis.
Mixture: This impure form is made up of several different kinds of atoms or molecules.
A mixture is, for instance, sodium chloride and water.
As a result, (C), a single, irreducible component, is the right answer.
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KINDLYY FASTT A uniform metre rule of mass 100 g is pivoted at the 60 cm mark. At what point on the meter rule should a mass of 50 g be suspended for it to balance horizontally?
Answer:
80 cm.
Explanation:
Since the metre rule is 1 m i.e 100 cm it means that the mass of the metre can be obtained at the 50 cm mark.
But the metre is pivoted at the 60 cm.
Please refer to the attached photo for details.
In the attached photo, y is the distance between the mark (that will balance the metre rule when a 50 g mass is hunged) and the pivot.
Thus, we can obtain the value of y as follow:
Anticlock wise moment = Clock wise moment
Anticlock wise moment = 100 × 10
Clock wise moment = y × 50
Anticlock wise moment = Clock wise moment
100 × 10 = y × 50
Divide both side by 50
y = (100 × 10) /50
y = 20 cm
Now, to obtain the mark, B that will balance the metre, we simply add 20 cm to 60 cm ie
B = 60 + 20
B = 80 cm
Which two possible explanations does the video give for why white light changes into colored light? Color is an impurity added to white light by the prism. Color is present in the materials on which white light shines. White light contains seven colors, which are separated by the prism. White light reacts with chemicals in the air to produce seven colors.
Answer:
White light contains seven colors, which are separated by the prism.
White light reacts with chemicals in the air to produce seven colors.
Explanation:
It was first observed by Sir Issac Newton, that when white light is passed through a prism, an elongated, coloured patch of light is obtained on a screen placed behind the prism. The seven colours obtained constitute the spectrum of white light.
In nature, white light is separated into its constituent wavelengths when white light interacts with substances in the atmosphere.
Answer:
The correct answer is “color is an impurity added to white light by the prism.”
and
“White light contains seven colors, which are separated by the prism
Explanation:
what type of image is formed by a lens if m = -0.87
A. The image is larger than the object and the image is real
B. The image is smaller than the object and the object is real
C. The image is larger than the object and is virtual
D. The image is smaller than the object and is virtual
Answer:
B.
Explanation:
as there is a '-' sign before the magnification value, it forms a real image.
so the last two options get cancelled.
as the value of magnification is 0.87 ie. lesser than 1, we can say that the image is smaller.
The type of image is formed by a lens if m = -0.87 would be smaller than the object and the object is real
What is a lens?A lens is a transmissive optical tool that employs refraction to focus or disperse a light beam. The power of the lens is expressed in the dioptre which is the reciprocal of the focal length of the lens.
The image formation through the lens is calculated with the help of the lens formula given as follows
1/f = 1/v - 1/u
where f is the focal length of the lens
u is the distance of the object from the lens
v is the distance of the image formed from the
magnification (m) = size of image /size of the object
As given in the problem image is formed by a lens if m = -0.87
Thus, the negative sign represents that the image formed by the object is real, and the magnitude of the magnification is less than 1 this represents that size of the image is smaller than the size of the object.
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what is acceleration produced by a force of 12 newton exerted on an object of mass 3kg
Answer:
a=F/m
a=12N/3kg (here newton can be written as kgm/s^2 so kg will be cancelled)
a=4m/s^2
Explanation:
What is the function of a heart rate monitor?
O to monitor blood pressure
O to track abnormal heart rhythm
O to estimate VO2max
O to track how fast a heart beats
Answer:
O- to track how fast a heart beats
Explanation:
3) An earth moving machine uses diesel oil, which when burnt will produce 3.0x10 9 J of energy. The work performed by the machine is 2.7x 10 8 J. What is the efficiency of the machine?
Answer:
The answer is below
Explanation:
The efficiency of a machine is the ratio of its output to its input. The efficiency shows how effective the machine by the way it converts the input energy into work. The higher the efficiency of the machine the more effective it is. The efficiency is usually less than 1.
Given that the machine uses diesel oil (input) that can produce 3.0 x 10⁹ J of energy while the work performed by the machine (output) is 2.7 x 10⁸ J. The efficiency is given as:
Efficiency = output / input = 2.7 x 10⁸ J / 3.0 x 10⁹ J = 0.09 = 9%
This means that the machine is not effective because of its low efficiency
A mobile starts with a speed of 250m / s and begins to decelerate at a rate of 3m / s². How fast is it after 45s?
[tex] \large{ \underline{ \underline{ \bf{ \purple{Given}}}}}[/tex]
Speed of the mobile = 250 m/sIt starts decelerating at a rate of 3 m/s²Time travelled = 45s[tex] \large{ \underline{ \underline{ \bf{ \green{To \: find}}}}}[/tex]
Velocity of mobile after 45 seconds[tex] \large{ \underline{ \underline{ \red{ \bf{Now, \: What \: to \: do?}}}}}[/tex]
We can solve the above question using the three equations of motion which are:-
v = u + ats = ut + 1/2 at²v² = u² + 2asSo, Here a is acceleration of the body, u is the initial velocity, v is the final velocity, t is the time taken and s is the displacement of the body.
[tex] \large{ \bf{ \underline{ \underline{ \orange{Solution:}}}}}[/tex]
We are provided with,
u = 250 m/sa = -3 m/s²t = 45 sBy using 1st equation of motion,
⇛ v = u + at
⇛ v = 250 + (-3)45
⇛ v = 250 - 135 m/s
⇛ v = 115 m/s
✤ Final velocity of mobile = 115 m/s
━━━━━━━━━━━━━━━━━━━━
certain atom has 86 protons. Assume that the nucleus is a sphere with radius 6.98 fm and with the charge of the protons uniformly spread through the sphere. At the nucleus surface what are (a) the magnitude and (b) direction (radially inward or outward) of the electric field produced by the protons?
Answer:
a. [tex]2.54 \times 10^{21} NC^{-1}[/tex]
b. Outwards
Explanation:
The computation is shown below:
a. The magnitude could be computed by applying the following formula
Electric field, E is
[tex]= \frac{kq}{r^{2}} \\\\ = \frac{9\times10^{9} \times86\times1.6\times10^{-19}}{(6.98\times10^{-15})^2}[/tex]
[tex]= 2.54 \times 10^{21} NC^{-1}[/tex]
b. As we can see that there is a positive charge so the direction would be in the outward direction in the electric field i.e. produced by the protons
Basically we applied the above formula for the first part
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Answer: 9.675 Hz .
Explanation:
Given, velocity of waves = 12.9 m/s
Length of string = 2.00 m
Let [tex]\lambda[/tex] be the wavelength , then for 3 loops
[tex]\dfrac{3}{2}\lambda= \text{length of string}\\\\\Rightarrow\ \dfrac{3}{2}\lambda= 2\ m\\\\\Rightarrow\ \lambda= \dfrac{4}{3}\ m[/tex]
Now , velocity = frequency x wavelength
Then, frequency = [tex]\dfrac{velocity}{wavelength}[/tex]
[tex]=\dfrac{12.9\times3}{4}\\\\=9.675\ Hz[/tex]
hence, it will create standing waves with 3 loops at 9.675 Hz .
Read the article, "Does Science Never Absolutely Prove Anything?" Then consider the theory of evolution. Do you consider the theory of evolution proven, evolving, or borderline science? Support your answer.
Answer:
Explanation:
Evolution/Advancement on the off chance that you see,then you will find this is a definitive revelation of science.It demonstrated that how people came into the world.How different creatures endure and from where they have hit on where they are today.All such things are the piece of development process.
New things advanced consistently from the past one and its a slow process.For anything to sprout you need a seed.As per the scientist,evolution is a reality and it is a steady procedure and it is happening.There are scarcely any situations where in the old harvest can yield new assortment as well.This is something many refer to as advancement only.Its a ceaseless process.Whatever comes,it accompanies certain misstep or zones of improvement,so if there happens to be a few changes would prompt improvement of new thing.
In the event that you see at an early stage,worms were available ,from where the fish came,then some went ahead land and began adjusting the progressions require to make due on land,started strolling on legs,developed lungs,then likewise there were advancement of the considerable number of things require to proceed with the life.All are the piece of development as it were.
hence,Darwin said,that natural selection can prompt evolution.This is likewise evident that so as to address the issue of food and nutrition,everybody works and as long as you get those needs,there will be development in all aspects.Similarly happened to the antiquated occasions when advancement occurred.
Hence,The development is truth and is a continuous procedure according to the science.When you go to demonstrate some case,there are consistently a point from where new methodology can be shaped and can prompt another disclosure.
If we consider the theory of evolution then we can say that it’s a proven theory, the reason people says that scientists don’t prove anything is because of the fact that they always implement “Precautionary principle” in their research finding.
Answer:
.
Explanation:
Is there a way for us to control motion
Answer:
They are:
1) change position
2) distract yourself
3) Get fresh air
4) Face the direction you are going.
5) Drink water.
6) Play music.
7) Put your eyes on horizon.
Explanation:
Hope it helps.
The probe used in a medical ultrasound examination emits sound waves in air that have a wavelength of 0.12 mm. What is the wavelength of the sound waves in the patient?a) 0.54 mm b) 0.12 mm c) 0.26 mm d) 0.027 mm
Answer:
0.54mm
Explanation:
Given the following :
Wavelength (λ) of Soundwave in air = 0.12mm
Velocity of sound wave (v) = 340m/s
Calculate the frequency (f) :
v = fλ
Wavelength to metres
1000mm = 1 m
0.12mm = (0.12/1000)m
= 0.00012m
v = fλ
340 = F * 0.00012
f = 340 / 0.00012
f = 2833333.3 Hz
Wavelength of Soundwave in the patient:
Velocity of sound wave through body tissue = 1540m/s
Therefore,
Using v = fλ
λ = v / f
λ = 1540 / 2833333.3
λ = 0.0005435m
λ = (0.0005435 * 1000)mm
λ = 0.5435mm = 0.54mm
The distance between neighbouring, identical wave components, such as adjacent compressions, determines a sound's wavelength. The number of waves passing a spot in a given amount of time is known as the frequency, which is the same as the source's frequency.
What wavelength of the sound waves in the patient?Wavelength (λ) of Soundwave in air = 0.12 mm
Velocity of sound wave (v) = 340m/s
Calculate the frequency (f) :
v = fλ
Wavelength to metres
1000 mm = 1 m
0.12 mm = (0.12/1000)m
= 0.00012 m
v = fλ
340 = F × 0.00012
f = 340 / 0.00012
f = 2833333.3 Hz
Wavelength of Soundwave in the patient:
Sound waves travel through body tissue at a speed of 1540 m/s.
Therefore, Using v = fλ
λ = v / f
λ = 1540 / 2833333.3
λ = 0.0005435m
λ = (0.0005435 × 1000)mm
λ = 0.5435mm = 0.54 mm
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Which best describes what happens if two waves meet and build on each other? constructive interference destructive interference reflection absorption
Answer:
Which best describes what happens if two waves meet and build on each other?
constructive interferencedestructive interference
reflection
absorption
Explanation:
When two waves meet in phase they will overlap together and form a constructive interference. The resultant amplitude of the waves will be greater than that of individual waves.
What is interference ?A wave of greater, lower, or the same amplitude is created when two waves merge through interference by combining their displacements at all points in space and time.
The interaction of waves that are coherent or correlated with one another, either because they originate from the same source or because their frequencies are similar or almost identical, leads to both constructive and destructive interference.
All sorts of waves, including light, radio, acoustic, surface water waves, gravity waves, and matter waves, can exhibit interference effects. In constructive interference, the waves are in single phase forms a resultant wave with higher amplitude.
When waves from out of phase meets, the resultant wave will have an amplitude less than the individual amplitudes. Here, the waves are meet in phase and build on each is constructive interference.
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A balloon is ascending at the rate of 4.9 m/s. A packet is dropped from from the balloon when situated at a height of 100m.
How long does it take the packet to reach the ground ?
What is it's final velocity ?
Answer:
Explanation:
Initially the packet was ascending up with the balloon.
Taking upward as positive direction;
initial velocity, u = 4.9 m/s
final velocity = v m/s
initial height, h₁ = 100 m
final height, h₂ = 0
a = -9.8 m/s²
time taken = t seconds
Considering the second equation of motion.
S = ut + 1/2at^2
s = ut + 0.5at²
(h₂-h₁) = ut + 0.5at²
0- 100 = 4.9t + 0.5×(-9.8)×t²
-100 = 4.9t - 4.9t²
4.9t² -4.9t - 100 =0
t² -t - 20.41 = 0
Using : b±√(b²-4ac))/(2a).... 1
Where a =1, b = -1 c =-20.408
Substituting the values into equation 1
Solving it, we get t = 5.045s
v = u + at = 4.9 -9.8×5.045 = 4.9 - 49.44 = -44.54 m/s
The final velocity is -44.54 m/s, and it took 5.045s to reach the ground.
Seje
A burning electric bulb is a good example of a(an)... object.
2 points
illuminated
luminous
translucent
transparent
Clear selection
Can you help me answer this pls
Answer:
luminous bcz they emits light by their own and don't need other resources to emit light
What are the chances that radio transmissions from Earth or messages sent on distant space probes will ever be received by living beings
Answer:
Very low
Explanation:
It is fair to say to a reasonable extent that there are very low chances that radio transmissions from Earth or messages sent on distant space probes will ever be received by living beings .
Bear in mind that for years some scientists have believed without any substantial evidence that there are other living beings in distant space.
If the reading of a linear scale is 4 mm and no of division of the circular scale is 50, then what will be the diameter of the wire in mm? (Least count = 0.01) * 2 points 2.25 3.5 4.5 9.0
Answer:
Diameter of Wire = 4.5 mm
Explanation:
First, we need to find the fractional part of the reading. The fractional part o the reading can be given by the following formula:
Fractional Part = Circular Scale Reading x Least Count
where,
Circular Scale Reading = 50
Least Count = 0.01 mm
Therefore,
Fractional Part = (50)(0.01 mm)
Fractional Part = 0.5 mm
Now, the diameter of the wire can be given by using the following formula:
Diameter of Wire = Linear Scale Reading + Fractional Part
Diameter of Wire = 4 mm + 0.5 mm
Diameter of Wire = 4.5 mm
To see if your results are reasonable, you can compare the final velocity of the stone as it falls down unwinding the wire from the pulley, to the velocity the stone would have if falling the same distance while unconnected to the pulley. What is the velocity of an untethered stone after falling 0.337 m from rest
Answer:
The velocity of the stone is 2.57 m/s.
Explanation:
Given that
Height = 0.337 m
We need to calculate the velocity of the stone
Using equation of motion
[tex]v^2-u^2=2gh[/tex]
Where, v = velocity of stone
u = initial velocity
g = acceleration due to gravity
h = height
Put the value into the formula
[tex]v^2-0=2\times9.8\times 0.337[/tex]
[tex]v=\sqrt{2\times9.8\times0.337}[/tex]
[tex]v=2.57\ m/s[/tex]
Hence, The velocity of the stone is 2.57 m/s.
A car is driving at 99 km/h, calculate the distance it travels in 70 minutes.
Give your answer in correct SI units rounded to 0 decimal places.
Answer:
The distance the car travels is 115500 m in S.I units
Explanation:
Distance d = vt where v = speed of the car and t = time taken to travel
Now v = 99 km/h. We now convert it to S.I units. So
v = 99 km/h = 99 × 1000 m/(1 × 3600 s)
v = 99000 m/3600 s
v = 27.5 m/s
The speed of the car is 27.5 m/s in S.I units
We now convert the time t = 70 minutes to seconds by multiplying it by 60.
So, t = 70 min = 70 × 60 s = 4200 s
The time taken to travel is 4200 s in S.I units
Now the distance, d = vt
d = 27.5 m/s × 4200 s
d = 115500 m
So, the distance the car travels is 115500 m in S.I units
Figure 3 shows a stationary metal block hanging from the middle of a stretched wire which is suspended from a horizontal beam. The tension in each half of the wire is 15 N. (a) Calculate for the wire at A, (i) the resultant horizontal component of the tension forces, (ii) the resultant vertical component of the tension forces. Can someone explain why the first one is 0?
Explanation:
(i) The horizontal component of the tension in the right wire points right, and the horizontal component of the tension in the left wire points left. Since these components are equal and opposite, the resultant horizontal force is 0.
∑Fₓ = 15 N cos 20° − 15 N cos 20°
∑Fₓ = 0 N
(ii) ∑Fᵧ = 15 N sin 20° + 15 N sin 20°
∑Fᵧ = 10.26 N
i) The resultant horizontal component of the tension forces is 0N
ii) The resultant vertical component of the tension forces is 10.26N
iii) The sum of force along the horizontal is zero because the force has the same magnitude and moving in the opposite direction.
i) From the given figure, the horizontal component of the force is given as;
[tex]F_x = + 15 cos 20^0 + (-15cos20^0)\\F_x = + 15 cos 20^0 -15cos20^0\\F_x =0[/tex]
The sum of force along the horizontal is zero because the force has the same magnitude and moving in the opposite direction.
ii) The vertical component of the force is expressed as
[tex]F_y = + 15 sin 20^0 + 15sin20^0)\\F_y = 2(15sin20^0)\\F_y=2(5.13)\\F_y=10.26N[/tex]
Hence the resultant vertical component of the tension forces is 10.26N
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On which factor mechanical advantage of simple machine depend on? Please help me and perfect answer will be brainlest answer.
Answer:
The factor that determines the mechanical advantage (or ideal mechanical advantage (IMA) - in the absence of frictional forces) in a simple machine is the ratio perpendicular distance of the applied force to the fulcrum to the perpendicular distance of the load to the fulcrum
The mechanical advantage can therefore by larger than 1 (requiring less force per load), or equal to 1 (effort equal to load) or less than 1( effort more than load)
Explanation:
How can you define a solution to an equation?
Which statement correctly describes the quantitative relationship between acceleration and net force on an object shown in the data table? (1 point) When the net force applied to an object changes, the mass of the object remains constant. When the net force applied to an object changes, the acceleration changes by a different factor. When the net force applied to an object changes, the mass of the object also changes. When the net force applied to an object changes, the acceleration changes by the same factor.
Answer:
The correct answer is A
Explanation:
Because when the net force applied to an object changes, the acceleration changes by the same factor. This answer is correct and I hope it helps you too.Hope this helps....
Have a nice day!!!!
The statement that correctly describes the quantitative relationship between acceleration and the net force on an object shown in the data table is as follows:
When the net force applied to an object changes, the acceleration changes by the same factor.Thus, the correct option for this question is D.
What is Acceleration?Acceleration may be defined as a type of rate at which the velocity of an object may change with respect to time. This change in velocity may come in terms of both speed and direction. Acceleration is a type of vector quantity because it has both magnitude and direction.
According to the context of this question, when the net force applied to an object may change, the acceleration may also change. This change is significantly induced by the same factor. This is because the acceleration of an object may directly rely on the net force applied.
Therefore, when the net force applied to an object changes, the acceleration changes by the same factor. Thus, the correct option for this question is D.
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An eletric pump in the ground floor
building taken 15 then to fill
a tank of volume 300
3003 with water
If the tank in 40met above the ground
and the efficiency of the pump
not
find the electric power consumed by
the pump in filling
the tank
Answer:
The input power is [tex]44.4\times10^{3}\ kW[/tex]
Explanation:
Given that,
Time = 15 min
Volume of water = 30 m³
Height = 40 m
Efficiency = 30%
Density of water = 1000 kg/m³
Suppose, acceleration due to gravity = 10 m/s²
We need to calculate the mass of water pumped
Using formula of mass
[tex]Mass = Volume\times density[/tex]
Put the value into the formula
[tex]Mass=30\times1000[/tex]
[tex]Mass=3\times10^{4}\ kg[/tex]
We need to calculate the output power
Using formula of power
[tex]P_{out}=\dfrac{W}{t}[/tex]
[tex]P_{out}=\dfrac{mgh}{t}[/tex]
Put the value into the formula
[tex]P_{out}=\dfrac{3\times10^{4}\times10\times40}{15\times60}[/tex]
[tex]P_{out}=\dfrac{4}{3}\times10^{4}\ Watt[/tex]
We need to calculate the input power
Using formula of efficiency
[tex]\eta=\dfrac{P_{out}}{P_{in}}[/tex]
[tex]P_{in}=\dfrac{P_{out}}{\eta}[/tex]
Put the value into the formula
[tex]P_{in}=\dfrac{4\times100\times10^{4}}{3\times30}[/tex]
[tex]P_{in}=\dfrac{4\times10^{5}}{9}\ Watt[/tex]
[tex]P_{in}=44.4\times10^{3}\ kW[/tex]
Hence, The input power is [tex]44.4\times10^{3}\ kW[/tex]
