If the pendulum is taken into orbiting space it will continue to oscillate in a vertical plane with the same period.
Oscillation is the repetitive or periodic variation, normally in time, of some degree about a central price or among two or extra exclusive states. Acquainted examples of oscillation include a swinging pendulum and alternating present-day.
Oscillatory movement is defined because of the to and fro movement of the body about its constant function. An oscillatory movement is a form of periodic motion. Examples of oscillatory motion are vibrating strings, swinging of the swing, and so on.
As the pendulum acts closer to the other quit of its swing, all of the kinetic energy turns returned into potential power.
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If you drop a ball from 3.1 m, what is its speed as it hits the ground?
Answer:
Zero I think I'm not sure
When you cook a marshmallow on a metal poker tool over an open flame, energy is transferred. Identify the three different ways thermal energy is transferred in this situation. Be sure to name the specific places or phenomenon in this system where each of the types of thermal energy transfer is occurring and the direction the energy is being transferred (from what to what).
When we cook a marshmallow on a metal poker tool over an open flame, there are three ways in which heat energy is transferred: Conduction, convection, and radiation.
Heat energy transferHeat transfer is the natural transfer of heat from an object with a higher temperature to an object with a lower temperature. Heat transfer can occur in three ways, namely conduction, convection, and radiation.
Conduction occurs when heat flows from a place with a high temperature to a place with a lower temperature using a fixed heat-conducting medium. Heat transfer from the open flame to the marshmallows via direct fire contact with the marshmallows is an example of conduction.Convection is the transfer of heat by means of a stream in which the intermediate substance also moves. If the particles move and cause heat to propagate, convection will occur. The hot air rising from the flames burning the marshmallows is an example of convection.Radiation is heat transfer without a medium. Radiation can also usually be accompanied by light. The direct transfer of heat from the flame to the marshmallow in the form of waves is an example of radiation.Learn more about heat transfer here: https://brainly.com/question/16055406
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which method of measuring distances would you use if you wanted to measure the distance to stars in a nearby galaxy?
Parsec is used to measure the distances of stars in a galaxy.
A galaxy is a gadget of stars, stellar remnants, interstellar fuel, dirt, and darkish count number, certain together by means of gravity. The phrase is derived from the Greek galaxies, actually 'milky', a connection with the Milky manner galaxy that contains the solar gadget.
In 2021, information from NASA's New Horizons area probe turned into used to revise the sooner estimate to kind of two hundred billion galaxies.
The smallest of galaxies incorporate a “mere” few hundred million stars while the biggest galaxies contain up to a hundred trillion stars! Scientists have been able to segment galaxies into 4 principal types: spiral, elliptical, abnormal, and abnormal.
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the air around a pool and the water in the pool receive equal amounts of energy from the sun. why does the air experience a greater increase in temperature than does the water?
The air around a pool and the water in the pool absorb the same amount of energy from the sun; however, the water requires more energy to increase its temperature than the air does.
The Differences in Temperature Increase between Air and Water in Response to Solar EnergyWater has a higher specific heat capacity than air, meaning it requires more energy to increase its temperature by the same amount. This is because the molecules in water are more tightly bonded than those in air, so more energy is needed to break these bonds and increase the temperature.
Additionally, water has a higher latent heat of vaporization than air, meaning it requires more energy to evaporate and create steam. Therefore, the air experiences a greater increase in temperature than the water.
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Kent Swimm (who is taking physics for the second year in a row, and not because he likes it) has
rowed his boat to within three feet of the dock. In an effort to save a little time, he decides that he
will simply jump off his boat onto the dock, turn around and then tie down his boat. Explain to
Kent why this would not be too wise an idea.
Answer:
The boat moves away from the dock, he won't be able to grab the line
Explanation:
When he jumps, he applies a force to the boat and the boat exerts a force equal in magnitude and opposite in direction to the force he applied. Because the friction is very low between the bottom of the boat and the water, the boat moves away from the dock. He won't be able to lean over and grab the line. This is Newton's 3rd Law of Motion.
what is the net torque on the wheel due to these three forces for an axis perpendicular to the wheel and passing through its center? let counterclockwise torques be positive.
The magnitude of the net torque on the wheel due to these three forces for an axis perpendicular to the wheel and passing through its center is
¹/₂MR³a.
What would be the Net torque on the wheel?The net torque on the wheel is determined from the moment of inertia of the pulley and the angular acceleration.
∑τ = Iα
where;
I is moment of inertia α is angular accelerationthe moment of inertia of the axis perpendicular to the wheel and passing through its center is calculated as;
I = ¹/₂MR²τ = ¹/₂MR²ατ = ¹/₂MR²(aR)τ = ¹/₂MR³awhere;
a is the acceleration due to the applied force.
Thus, the magnitude of the net torque on the wheel due to these three forces for an axis perpendicular to the wheel and passing through its center is ¹/₂MR³a.
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What is the difference expressed in kilograms between the mass of a proton and an electron.
The difference between the mass of a proton and an electron is 9.99 X 10⁻²⁸ Kg.
Mass of a proton = 1.67 X 10⁻²⁴ g
Mass of an electron = 9.1 X 10⁻²⁸ g
Converting Mass to Kilogram,
Conversion factor: 1kg = 1000 g
Mass of a proton = 1.67 X 10⁻²⁷ g
Mass of an electron = 9.1 X 10⁻³¹ g
Difference in their masses would be,
= Difference = Mass of proton - Mass of electron
= Difference = ( 1.67 X 10⁻²⁷ ) - ( 9.1 X 10⁻³¹ )
= Difference = 9.99 X 10⁻²⁸ Kg
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a color television tube also generates some x rays when its electron beam strikes the screen. what is the shortest wavelength of these x rays, if a 30.0-kv potential is used to accelerate the electrons?
6.626 x [tex]10^{-11}[/tex] m is the shortest wavelength of these x rays.
Solution:
λ = h c/ΔE
λ = wave length
h = 6.626 x [tex]10^{-34}[/tex] m² kg /s = Planck constant
ΔE = 30 keV potential ( 1 keV = 1.6021 x [tex]10^{-16}[/tex] J)
c = velocity of light = 3 x 10⁸ m/s
Put these values in formula,
λ = (6.626 x [tex]10^{-34}[/tex] m² kg /s x 3 x 10⁸ m/s) / (30 x 1.6021x [tex]10^{-16}[/tex] J)
= 6.626 x [tex]10^{-11}[/tex] m
Hence, 6.626 x [tex]10^{-11}[/tex] m is the shortest wavelength of these x rays.
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how does the difference between the ranges of the strong nuclear force and the coulomb force affect the makeup of each atom’s nucleus?
The strong force, which is thought to hold atoms' nuclei together and is even stronger than the Coulomb force at close ranges, was postulated by physicists as a result of Coulomb's law inside the nuclei of atoms.
The strong nuclear force's extremely limited range is what makes it so challenging to produce nuclear fusion on Earth.According to Coulomb's law, the square of the distance between two charges has an inverse relationship with the electrical force of attraction or repulsion between them.Charles-Augustin de Coulomb, a French physicist, first described this force as the Coulomb force in 1785. Because of this, the law was called in his honor and served as the foundation for electrostatics.To know more about Coulomb force
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f io is the intensity of the light incident on the first polarizer, what is the intensity of the light that passes through the second polarizer whose axis is oriented at an angle of 90 degree
The second polarizer's axis is positioned at a 90-degree angle, and the light intensity that passes through it is 0.
The incident light is ordinary light. it is unpolarised
I₁=I₀/2 For the first polarized
I₂=I₁cos²θ (Second polarization)
=I₀/2 cos²90° (θ=90)
=I₀/2(0)²
=0
When an area is measured on a plane perpendicular to the direction of energy propagation, it is possible to define the intensity or flux of radiant energy as the power transferred per unit area. Watts per square meter (W/m2) and kg/s3 are the basic units for this system in the SI. The term "intensity" is most usually used to describe electromagnetic or acoustic waves, such as light or radio waves, where the average power transfer over the course of one wave period is taken into account. Any situation where energy is exchanged can be described as having intensity. The amount of kinetic energy that water drops from a garden sprinkler are carrying, for instance, might be calculated.
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A student pushes a 12-kg block on a frictionless, horizontal surface. If the block is initially at rest, what is the speed of the block after the student pushes the block for 5 seconds with an acceleration of 2. 0 m/s/s?.
The speed of the block after the student pushes it is 10m/s.
Mass of the block = 12 Kg
Initial speed = u = 0 m/s
Time = t = 5 s
Acceleration = a = 2 m/s²
Final speed = v =
To determine the final velocity; we use the First Equation of Motion:
= v = u + at
= final speed = initial speed + acceleration X time
= v = 0 + 2 X 5
= v = 10 m/s
Therefore, the speed of the block after the student pushes it for the time period of 5 s with an acceleration of 2 m/s² is 10m/s.
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What is the wavelength of a wave with period 2 s and speed 2 cm s?
The speed of the travelling wave is found to be 0.0628m.
The time period is given to be 2 seconds.
The time period and the frequency are related as,
T = 2πv
Putting values,
2 = 2πv
v = 1/π Hz.
The relationship between the frequency of the wave, the wavelength of the wave and the speed of the wave is given by
V = fy
Where,
V is the speed of the travelling wave,
F is the frequency of the travelling wave,
y is the wavelength of the travelling wave.
The speed of the travelling wave is given to be 2 cm/s (0.02m/s) and the frequency of the travelling wave is 1/π.
Now, putting all the values,
0.02 = 1/πy
y = 0.0628m
So, the wavelength of the travelling wave is 0.0628m.
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the hubble constant is about 70 km/s/mpc. you measure the redshift of four galaxies. the first has a redshift of 1500 km/s, the second has a redshift of 750 km/s, the third has a redshift of 5000 km/s and the fourth has a redshift of 2000 km/s. which galaxy is the closest?
The hubble constant is about 70 km/s/mpc. you measure the redshift of four galaxies. the first has a redshift of 1500 km/s, the second has a redshift of 750 km/s, the third has a redshift of 5000 km/s and the fourth has a redshift of 2000 km/s. Andromeda is the closest galaxy.
A galaxy is made up of gravitationally bound clusters of stars, stellar debris, interstellar gas, dust, and dark matter. The word "galaxias" is a Greek word that means "milky" and alludes to the Milky Way galaxy, which is where the Solar System is located. Hubble constant, galaxies range in size from dwarfs, which have less than 100 million stars, to supergiants, which have more than 100 trillion stars. All of these stars orbit the galaxy's center of mass. Galaxies have an average of 100 million stars. Stars and nebulae make up a very small portion of the material of a typical galaxy; dark matter makes up the majority of the galaxy's mass. Typically, galaxy cores contain supermassive black holes. Galaxies can be characterized as elliptical, spiral, or irregular based on their visual shape. [6] Many of them are thought to have supermassive black holes in their cores. The main black hole of the Milky Way.
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refer to the accompanying photos of an elliptical galaxy and a spiral galaxy to answer the following: which image (a or b) is an elliptical galaxy? which of these galaxies appears to contain more young, hot, massive stars? how did you determine your answer? when stars are born from a cloud of dust and gases, high- and low-mass stars form at about the same time. which group of stars, high-mass or lowmass, will die out first? over time, how will this affect the color of the light we observe coming from this group of stars?
Answer:
An elliptical galaxy is a type of galaxy in the Hubble sequence characterized by having a roughly ellipsoidal shape and hardly any distinctive features, lacking, for example, the spiral arms that characterize the homonymous galaxies. They are one of the four main classes of galaxies described by Edwin Hubble in his 1936 work The Realm of the Nebulae,1 along with spiral and lenticular galaxies. Elliptical galaxies (E) are, along with lenticular galaxies (S0) with their large-scale disks, and ES234 galaxies with their intermediate-scale disks, a subset of the "early-type" galaxy population. ".
Most elliptical galaxies are composed of older, low-mass stars, with a sparse interstellar medium and minimal star formation activity, and tend to be surrounded by large numbers of globular clusters. Elliptical galaxies are thought to make up about 10-15% of the galaxies in the Virgo Supercluster, and are not the dominant galaxy type in the universe as a whole.5 They are found preferentially near the centers of galaxy clusters .6
Elliptical galaxies range in size from dwarf ellipticals with tens of millions of stars, to supergiants with over a hundred trillion stars dominating their galaxy clusters. Originally, Edwin Hubble hypothesized that elliptical galaxies evolved into spiral galaxies, which was later found to be false,7 although the accumulation of gas and smaller galaxies can form a disk around a pre-existing ellipsoidal structure.8 9 The stars found within elliptical galaxies are, on average, much older than the stars found in spiral galaxies.7
Explanation:
What is the wavelength of radiation that has a frequency of 2.10 1014 s?
The wavelength of radiation is 1.428 x 10⁻⁶m.
The equation E=hf is called the Planck relation or Planck-Einstein relation. The letter h is named after Planck as Planck's constant. Energy (E) is related to this constant h and the frequency (f) of the electromagnetic wave.
In quantum wave theory, the Planck relation describes the shear wave energy emitted or absorbed as an electron transitions between energy levels within an atom. If the atom contains electrons, the destructive wave interference between the protons and electrons in the nucleus gives rise to destructive waves, resulting in binding energy. This binding energy is the energy of a photon emitted when an electron is captured or moves between states within an atom. Electron vibrations generate transverse waves, and photon energy is based on the frequency of that vibration.
c/y=v
c/v=y
3 x 10⁸/2.10 x 10¹⁴
1.428 x 10⁻⁶m
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1. a force of 125 N
while being moved 2.5 m. How much work is done?
The work is done by a force of 125 N while being moved 2.5 m is equal to 312.5 J.
What is the work?Work done can be described as the energy needed when a force is applied to move an object through a definite displacement. The work done can be defined as both the applied force and the displacement of the object.
The function of the force is to move a body in a straight line in the direction of the exerted force over a distance 'd'.
W= F × d
Where 'd' is the displacement, 'F' is the applied force and W is the work done.
Given, the force applied on the object, F 125 N
The displacement by the object, d = 2.5 m
The work done by the object can be calculated as:
W = F.d
W = 125 ×2.5
E = 312.5 J
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four charges q1, q2, q3 and q4, are placed at the corners of a square. charges q1 and q4 are located on opposite corners and have equal charges. both q2 and q3 have a charge of 1.0 c. if the force on q2 is zero, what is the charge on q1?
The charge on q1 if four charges q1, q2, q3 and q4, are placed at the corners of a square, and charges q1 and q4 are located on opposite corners and have equal charges is - 0.35 C.
Let the side of the square be a. Let the charges of q1 and q4 be q.
q2 = q3 = 1 C
The force on q2 due to q1 is,
F21 = ( k q2 q1 ) / a²
F21 = k q / a²
The force on q2 due to q4 is,
F24 = ( k q2 q4 ) / a²
F24 = k q / a²
Resultant of F21 and F24 is,
FR = √ ( F21² + F24²
FR = √ ( k q / a² )² + ( k q / a² )²
FR = √2 ( k q / a² )
The force on q2 due to q3 is,
F23 = ( k q2 q3 ) / ( √2 a )²
F23 = k / 2 a²
Since net force on q2 = 0
FR + F23 = 0
√2 k q / a² = - k / 2 a²
q = - 1 / 2 √ 2
q = - 0.35 C
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Entropy never decreases in a spontaneous process. Give an example to support this statement. n/a Now choose from one of the following options Why? a) The transfer of energy by heat from colder bodies to hotter bodies is a spontaneous process in which the entropy of the system of bodies increases. b The melting of an ice cube placed in a room causes an increase in the entropy of the room. c The dissolution of salt in water is a spontaneous process in which the entropy of the system increases. d) A plant uses energy from the Sun and converts it into sugar molecules by the process of photosynthesis.
The entropy never decreases in a spontaneous process. The correct example of this statement is (b) The melting of an ice cube placed in a room causes an increase in the entropy of the room.
The second law of thermodynamics can be stated in terms of entropy, in this statement of the law; ''a spontaneous process increases the entropy of the universe''. This is represented by the following equation:
ΔG = ΔH + TΔS
Where,
ΔG = Change in Gibb's Free Energy
ΔH = Change in heat
T = Temperature
ΔS = Entropy
If the value of ΔG = negative, then it is a spontaneous process. This is called exothermic process. In exothermic process, the entropy will only increase and in endothermic process, the temperature is high, so again the entropy will only increase.
Hence, entropy never decreases in spontaneous process.
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if a dipole, starting from rest and initially pointing opposite to an external magnetic field, is slightly perturbed, it will rotate in order to point in the same direction of the external magnetic field (its lowest potential energy state), with its potential energy changing to kinetic energy (just like a ball given a slight push at the top of a hill rolling into a valley). considering this energy conversion, what is the angular speed of the dipole moment as it passes through its lowest potential energy state (when it points in the same direction as the external magnetic field)?
When the angle between the dipole moment and electric field is 0°, the lowest amount of potential energy is present in an electric dipole.
What is the formula for magnetic dipole moments?Technically referred to as a magnetic dipole, a tiny current loop functions as a tiny magnet. The formula m = NIA, which results in the units - Ampere meter square, determines the power of that tiny magnet, the magnetic dipole moment m.
What is the relationship between an electron's rotating magnetic moment and angular momentum?The electron's orbital angular momentum forms a 180° angle with the orbital magnetic moment's direction. Explanation: Given is the equation for the relationship between an electron's rotational momentum and its magnetic moment: = - e m e L e 2 m e L, where e and me are the electron's mass and charges.
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it is estimated that there are a trillion comets in the oort cloud. if it extends out to about 50,000 au from the sun, what is the total volume of the oort cloud in cubic au? (for this calculation assume that the oort cloud is spherical in shape)
The volume of the oort cloud that is in the shape of sphere is 5.2 * 10¹⁴ au³.
We know the volume of sphere as V = 4/3 * (πr³)
where, V is the volume
r is the radius of the sphere
Given that, radius of oort cloud is r = 50000 au
The volume of the oort cloud can be calculated as follows.
V = 4/3 * (πr³)
π is substituted as 22/7
V = 4/3 * 22/7 * 50000³
⇒ 88/21 * 125 * (10⁴)³
⇒ 523.8* 10¹²
⇒ 5.238 * 10¹⁴
Hence, the volume of the oort cloud that is in the shape of sphere is 5.2 * 10¹⁴ au³.
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two bowling balls, a and b, each having a mass of 7.00 kilograms, are placed 3.00 meters apart. what is the magnitude of the gravitational force exerted by ball a on ball b?
The magnitude of the gravitational force exerted by ball A on ball B is equal to 36.31 × 10⁻¹¹ N.
What is gravitational force?Newton’s law of gravitation can be defined as every particle of matter in the universe attracting every other particle with mass with a certain force. The magnitude of gravitational force has a direct relationship with their masses.
Therefore, the gravitational force between two bodies can be written as:
[tex]\displaystyle F =G\frac{M_1M_2}{r^2}[/tex]
Where G denotes the universal gravitational constant.
Given, the mass of the Ball A = Ball B = 7 Kg
The separation between the two balls, r = 3 m
The magnitude of the gravitational force applied by ball A on ball B can be determined as:
[tex]\displaystyle F =6.67 \times 10^{-11} \times \frac{7\times 7}{(3)^2}[/tex]
F = 36.31 × 10⁻¹¹ N
Therefore, the gravitational force is equal to 36.31 × 10⁻¹¹ N.
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The two-neuron chain allows increased communication and control of the effector organ. True/False?
The two-neuron chain allows increased communication and control of the effector organ is true.
What are the two neurons that form the route from the CNS to the effector?Preganglionic and postganglionic neurons make up the link in the ANS between the CNS and its effector. Outside of the central nervous system, in an autonomic ganglion, is where these two neurons synapse.
The two-neuromuscular chain enables improved communication and regulates the effector organ. The sympathetic division is where the cell bodies of preganglionic neurons are found.
The brainstem or spinal cord of the central nervous system houses the preganglionic neurons' cell bodies (CNS).
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what property of light is responsible for the different colors we observe? different colors have different frequencies. the size of the photon determines the color. varying levels of intensity result in different colors. the speed of a light wave determines its color.
Wavelength is the property of light is responsible for the different colors.
The length that a periodic wave travels across in order to replicate its shape is known as its wavelength. It is the distance between two successive corresponding wave points of the same phase, such as two neighboring crests, troughs, or zero crossings, and it is a feature of both traveling waves and standing waves, as well as other spatial wave patterns. The spatial frequency is defined as the wavelength's inverse.. Additionally, sinusoidal wave envelopes, modulated waves, and waves created by the interference of several sinusoids are also commonly referred to as having a wavelength.
Wavelength. and frequency are inversely. related, assuming a sinusoidal. wave traveling at a constant. speed
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if 10.0 kg of ice at 0 o c is added to 2.0 kg of steam at 100 o c, the temperature of the resulting mixture is
If 2.0 kg of steam at 100 o C and 10.0 kilogram of ice at 0 o C are combined, the resulting mixture will be hotter than 50 degrees. In its gaseous state, water is steam.
This might happen as a result of boiling or evaporation, where heat is provided until the water achieves the enthalpy of vaporization. Although wet steam, the visible mist or aerosol of water droplets created as water vapour condenses, is sometimes referred to as "steam," saturated or superheated steam is invisible. The concept of temperature is used to convey quantitatively how hot and cold something is. Using a thermometer, one can gauge temperature. Thermometers are calibrated using a variety of temperature scales, which historically drew on a variety of reference points and thermometric substances.
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How is muscular strength calculated?
Muscle strength is measured by estimating a person's one repetition maximum (1RM).
1RM is a measurement of the greatest load (in kilograms) that one can move means it can be lifted, pushed, or pulled once without failure or injury.
1RM is calculated by counting the maximum number of exercises that you can do in repetition by the use of a load that is just less than the maximum amount that can be moved. This number is known as the repetitions to fatigue (RTF) – you are required to stop counting the repetitions when you feel you can no longer do the exercise in a proper way or when you slow down or can't keep a steady pace.
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justin, with a mass of 30 kg, is going down an 8.0-m-high water slide. he starts at rest, and his speed at the bottom is 11 m/s. how much thermal energy is created by friction during his descent?
537N thermal energy is created by friction during his descent.
The friction-related work is converted into thermal energy.
If Justin is initially at rest, MGH is his potential energy.
Thus, we have 30* 9.8*8 = 2352N.
Where,
Mass = m
Gravitational acceleration = g
Height = h
His potential energy is changed into usable kinetic energy when he reaches the bottom of the slide, leaving us with 1/2 mv^2.
Finally, we arrive to 1/2 * 30 * (11)^2 = 1815N
He had 2352N at the outset, and 1815N at the conclusion.
The thermal energy is therefore 2352 - 1815 = 537N.
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During a classroom lab activity, students built each of the circuits shown below and measured the current and resistance in each circuit. Each circuit contains a 1. 5-volt battery and each bulb has a resistance of 50 Ω.
When the switch is closed, in which circuit would resistance be the highest and current be lowest?
When the switch is closed, in the third circuit the resistance would be the highest and the current be the lowest.
From the question, we have
Voltage in the circuit, V = 1.5 volts,
The circuit's resistance, R = 50,
In the third diagram, the bulb is connected in parallel, which means that the voltage in the circuit will remain constant. Additionally, because the current depends on the resistor, the resistance in this circuit will be larger.
Additionally, according to Ohm's law, a high resistance will result in a low current flow.
Since there is only one bulb in the first circuit, resistance will be minimal and current flow will be high.
As a result, the third circuit's resistance would be the highest and its current the lowest when the switch is closed.
Current :
The phrase "electric current" is frequently used to describe how much electricity flows through a circuit and how it flows in an electronic circuit. Amperes are used to measure it (A). As more electricity passes through the circuit, the ampere value increases.
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When the switch is closed, in the third circuit the resistance would be the highest and the current be the lowest.
What is current?
When describing how much electricity flows through a circuit and how it flows in an electronic circuit, the term "electric current" is often employed. It is measured in amperes (A). The ampere number rises as more electricity flows through the circuit.
Given:
The Voltage in the circuit, V = 1.5 volts,
The resistance in the circuit, R = 50 Ω,
As you can see in the third diagram, there is a parallel connection of the bulb, so the voltage in the circuit will remain the same and the current depends on the resistor, so there will be higher resistance in this circuit.
And if the resistance is high the current flow will be low, (By Ohm's law)
In the first circuit, there is only one bulb, so resistance will be low, and the current flow will be high.
Therefore, when the switch is closed, in the third circuit the resistance would be the highest and the current be the lowest.
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A spherical balloon filled with gas has a leak that causes the gas to escape at a rate of 1. 5 m3/min. At what rate is the surface area of the balloon shrinking when the radius is 4 m? present your answer rounded to two decimal places.
Rate of change of surface area of the balloon shrinking is (3/4)m²/min when the radius is 4 m.
We are given that volume of spherical balloon is decreasing with a rate of 1.5m³/min. We know that volume of sphere is given by the formula=(4/3)πr³ where r is the radius of the spherical balloon.
We are given change of volume with respect to time, so we differentiate the volume with respect to time.
V=(4/3)πr³
=>dV/dt = (4/3)π×(3r²)×dr/dt
=>dV/dt=4πr²dr/dt
=>-1.5=4πr²×(dr/dt)
=>dr/dt = (-1.5/4πr²)m/min
Now, we know that surface area of sphere is given by the formula 4πr²,so we need we differentiate the surface area with respect to time again,
=>S=4πr²
=>dS/dt = 4π×2r×(dr/dt)
=>dS/dt = -8πr×(dr/dt)
We have dr/dt= (-1.5/4πr²),so putting it we get
=>dS/dt= -8πr×(-1.5/4πr²)
=>dS/dt = -(8×1.5)/(4×r)
when radius(r) is 4m,we get
=>dS/dt= -(8×1.5)/(4×4)
=>dS/dt= -12.0/16
=>dS/dt= -(3/4)m²/min
Hence, rate of change of surface area is (3/4)m²/min.
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is the current through r1 greater than, less than, or equal to the current through r2 immediately after the switch is first closed?
The ratio of current in both of the given resistors is I1 - R2
I2 R1
Here we have been given that two resistors which are and respectively are connected in parallel with a cell. We have been asked to find the current that is flowing through the resistor to the current flowing through
The current in both the resistors will be different as we know that in parallel connection of the given resistors the current through each of them is different, but the voltage remains the same.
From ohm's law, we have,
V = IR
Where V is the potential difference between the respective ends of the resistors, I is the amount of current flowing in the circuit and the R is the resistance.
Then we have,
Current (I1) in the resistor is as follows:
I1 =V/R1
Current (I2) in the resistor is as follows;
I2 =V/R2
The ratio of the currents in both the resistors is as follows;
I1/I2=V/R1
V/R2
⇒ I1/I2=R2/R1
Therefore the ratio of current in both the resistors is ⇒ I1/I2=R2/R1
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How is spring potential energy calculated?
The formula of string potential energy is equal to the product of force and distance of displacement.
Also, force is nothing but the product of spring constant and displacement.
The potential energy of the spring is calculated using the formula,
PE = 1/2* k* x²
where, k is spring constant
x is displacement
The potential energy of the spring is the potential energy stored as a result of the deformation of a particular elastic object, or a spring. It describes the work done to stretch a spring and depends on the spring constant k and the distance stretched.
The spring constant is the characteristic property of the spring. It depends upon the construction material and is measured in units of Nm⁻¹.
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