A hot iron sphere of 200g is kept in 500g of water at 10°C.As a result, the final temperature of water becomes 30°C.Find the initial temperature of the iron sphere.(specific heat capacity of iron =470J/kg°C.​

When an object is spinning around its center, as you move out from the center and the radius increases: the angular velocity decreases

The fact that the angular velocity of an object that is spinning around its center decreases as the object moves away from the center is due to the fact that as it moves away from the center the radius increases and because the relationship between radius and angular velocity is inversely proportional, as the radius increases the angular velocity decreases.

When an object is in uniform circular motion, the angle described by the radius in each unit of time is known as angular velocity. It is measured in units of (rad/s) (revolutions/s).

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a) The shoppers who walked from the car to the door in 20 minutes walked for 1200 seconds.

b) The shoppers' walking speed in meters per second is 0.67m/s.

A) In the question, we are already given how long it took for the shoppers to walk from their car to the entrance of the shopping mall, although it's in minutes. We are told that it took them 20 minutes to walk from their car to the entrance. In order to know how long they were walking in seconds, we would have to multiply by 60. This is because there are 60 seconds in one minute. Hence, to find the number of seconds in 20 minutes, we multiply 20 minutes by 60 seconds, thus;

                     20 minutes × 60 seconds = 1200 seconds.

B) Now that we know how long the shoppers were walking in seconds, we can use it to get their walking speed. To find the speed of any moving object, we divide the distance the object travelled by the time taken for the object to cross that distance in seconds. In the question, we are told that the shoppers parked their car 800 meters away from the entrance. This means that the distance they walked to get to the entrance is also 800 meters. Thus to find their walking speed;

                               Speed = distance ÷ time

                               Speed = 800 meters ÷ 1200 seconds

                              Speed = 0.67 m/s.

Therefore, the shoppers walked for 1200 seconds at 0.67m/s.

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The typical range of human hearing is 20 to 14,000 hz

Around 20 Hz to 20 kHz is the range of frequencies that humans can hear. However, as they become older, human infants lose some of their high-frequency sensitivity; the highest limit in ordinary adults is frequently closer to 15–17 kHz. Human neonates can actually hear sounds somewhat higher than 20 kHz. Although most speech frequencies fall between 100 and 4,000 Hz, the human ear can detect sounds between 20 Hz to 20,000 Hz (20 kHz).

Ultrasonic frequencies are those that are higher than 20,000 Hz. Many animals can hear ultrasonic frequencies even though they are outside the range of human hearing. A person with typical hearing may hear noises between 20 and 20,000 hertz (Hz). For voice processing, frequencies between 500 and 4000 Hz are crucial.

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The critical angle for this interface is closest is 45.6 degrees.

The refractive index is the velocity or the speed of the light through which the ratio is calculated by comparing that velocity to be present in the vacuum by its velocity in any specified medium which can be water or air and this medium is also called secondary medium and this medium should be greater density than the former one. The refractive index is represented by the letter 'n' and the value of the refractive index for air is 1.0003 and in the case of liquid the refractive index values can range from 1.0010 to 1.0060 and the formula for the refractive index calculation is n = c/v where n is the refractive index, c is the velocity or speed of light and v is the phase velocity of light that means when light is some other phase like liquid or air or refractive index can also be defined as the bending of the light when the light passes from one medium to other of different densities.

Given -

The Refractive index of crown glass is = 1.52

The Refractive index of water is = 1.33

The angle of incidence = 40°

To calculate the angle of refraction in water -

Using Snell's law

[tex]n_1 sin \theta i = n_2 sin \theta r[/tex]

[tex]n_1 / n_2 = sin \theta r/sin \theta i[/tex]

Where,

[tex]n_1[/tex] = Refractive index of crown glass

[tex]n_2[/tex] = Refractive index of water

[tex]\theta[/tex] i = incidence angle

Putting the value we will get

1.52 /1.33 = sin [tex]\theta[/tex]r / 40

sin [tex]\theta[/tex]r = sin 40 [tex]\times[/tex] 1.52 / 1.33

sin [tex]\theta[/tex] r = 0.715

So, theta r will be

[tex]sin^{-1}[/tex] ( 0.715 ) = 45.6 degrees.

Hence the correct answer is 45.6 degrees of the critical angle.

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Decane is an alkane with ten carbon atoms in its carbon chain. Hence, there are 22 hydrogen atoms.

Alkanes are acyclic, saturated hydrocarbons. Hydrocarbons are organic compounds made up of carbon and hydrogen only. Alkanes could be straight chained or branched.

Decane is a straight chained alkane with ten carbon atoms. To find the number of hydrogen atoms in any given alkane, we use the following molecular formular:

                    CₓH₂ₓ₊₂  

The x in the formular stands for the number of carbon atoms. The C represents carbon, and the H represents hydrogen. If we put ten in place of x in the formular, we would have:

                     C₁₀H₂₀₊₂

                   = C₁₀H₂₂

Therefore, Decane has 22 hydrogen atoms.

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A person skating on ice at a constant velocity is a static  situation in reference to biomechanics subdivisions

An interdisciplinary science known as biomechanics studies how organisms move and interact with their environment by applying physics concepts to biological systems. Biomechanics is interested in a wide range of motions, from small-scale, whole-body movements like a jumping cat to large-scale, complex movements like the contraction of muscles in cells. In order to characterize and comprehend the complex forces involved in biological systems, biomechanics utilizes the rules of physics with relation to levers, pulleys, and other known functions.

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The  helicopter flies 165m horizontally and then moves downward 45m below so ,the helicopter's resultant displacement is 171 m.

What is resultant displacement ?

Resultant displacement is defined as the the shortest distance from initial point of movement to the final point of movement.

What is Pythagoras theorem ?

Pythagoras theorem is defined for a right angled triangle as the square of the hypotonus being equal to sum of square of base and square of perpendicular.

given :

helicopter flies horizontally a displacement  (x) = 165m

helicopter flies vertically a  displacement  (y)= 45m

the above condition can be imagined in a 2-D graph or plane with x and y axis

and since the curve will be a sharp 90° the resultant figure is of a right angled triangle.

therefore,

using Pythagoras theorem we get;

( resultant displacement  )²= (165)² + (45)²

( resultant displacement  ) = 171 m

The  helicopter flies 165m horizontally and then moves downward 45m below so ,the helicopter's resultant displacement  is 171 m.

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Ka, Kb, and Ksp are all different types of equilibrium constants. The difference between these three is that Ka is the acid dissociation constant, Kb is the base dissociation constant and Ksp is the solubility product constant.

The relationship between a reaction's products and reactants with regard to a certain unit is expressed by the equilibrium constant, K. When an acid and its conjugate base are in equilibrium, Kb serves as the equilibrium constant, Ka is the acid equilibrium constant. Simply put, pKa is the -log of Ka.

Similar to this, Kb is the base dissociation constant and pKb is its -log. The moles per liter (mol/L) unit of measurement is commonly used to express the acid and base dissociation constants. The amounts of species present when ions are in equilibrium with undissolved salt are described by the solubility product (Ksp).

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The statements that accurately describe how physicists view the role of mathematics is: equations represent relationships between measurements; option 1

Mathematics is a branch of science that deals with numbers, formulas and related structures, shapes and spaces as well as the changes that occur in them.

Physics is a branch of science that studies matter, its constituents, motion and behavior through space and time, and their relation with energy and force.

The branches of Physics include:

Mathematics plays a very important role in physics as the equations of mathematics helps to explain relationship between measurements.

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The value in centimeters is [tex]1.44 \times 10^{-8}[/tex] cm.

Dimensional analysis is a method for changing a measurement's unit of measurement. A single unit of measurement can be multiplied by a number of fractions that, although expressed in different units, are essentially the same measurement.

A unit of measurement is a specific magnitude of a quantity that is adopted by law or convention and used as a standard for measuring other quantities of the same kind. Another amount of that type may be expressed as a multiple of the measuring unit.

Radius of gold =144pm

[tex]=144pm\times 1m/10^{12}pm[/tex]

[tex]=144 \times 10^{12} m[/tex]

[tex]=1.44 \times 10^{-10} m[/tex]

[tex]= 1.44 \times 10^{-8} cm.[/tex]

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Answer:

a

Explanation:

vector is size and direction

hope this works :)

The height of the cliff from the rock is thrown with an initial velocity of 8.00 m/s is: 45.8602 m

The formula for the downward vertical launch and the procedure we will use is:

y = V₀*t + (gt²) /2

Where:

Information about the problem:

With the information gave, we can calculate the height from the rock is thrown, using the formula of downward vertical launch:

y = V₀*t + (gt²) /2

y = (8.00 m/s * 2.35 s) + [9.8 m/s² *  (2.35 s)²] /2

y = 18.8 m + [9.8 m/s² * 5.5225 s²] /2

y = 18.8 m + [54.1205 m] /2

y = 18.8 m + 27.0602 m

y = 45.8602 m

In physics vertical launch is the motion described by an object that has been launched vertically in which the acceleration is the earth's gravitational force.

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Answer: At the top of a pendulum's swing, the ball is no longer moving (at that very specific point of time). All of its kinetic energy has been converted to potential energy (or more specifically in this instance, gravitational potential energy).

Explanation: hope this helps

Newton's law of universal gravitation tells us that all particles are attracted to each other with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of their distance apart. Hence, the answer to the question is true.

The statement on the question is in line with Newton's law of universal gravitation, which states that "the force of attraction between two objects with masses m1 and m2 is directly proportional to the product of their masses and inversely proportional to the square of their distance apart. The 'force of attraction' stated in the law the law is gravity. Mathematically, it is written as:

                         [tex]F= G\frac{m1*m2}{d^{2} }[/tex]

    where G is the universal gravitational constant.

This means that the force of gravity between two particles increases as the mass of the particles increase, and gravity exponentially reduces as the distance between the two particles increase.

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The net change in the internal energy is 40joules.

Given here, the force (F) = 800N acting over a distance of (D) = 0.05m(1cm = 0.01m)

First, we calculate work done by the formula,

Work done = Force × displacement

Work done = 800× 0.05

= 40joules.

Now, we calculate internal energy the first law of thermodynamics.

Internal Enegy (dE) =dQ + W

dE= 0+40

dE = 40joules.

Thus, internal energy was found to be +40joules.

Adiabatic process is a kind of thermodynamic process that takes place without the thermodynamic system or its surroundings exchanging heat or matter, in simple words it is defined as the system where no heat loss Or gained by the system.

An adiabatic process only transfers energy to the environment as work, as contrast to an isothermal process. The adiabatic process is a fundamental idea in thermodynamics and supports the law behind the first law of thermodynamics.

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The magnitude of the average acceleration of the car is  5.69 m/s², the distance (in m) the car travels in the first 7.20 s is 147.5 m an the speed of the car (in m/s) 10.0 s after it begins its motion will be 56 m/s.

Average acceleration is defined as the average rate of change of velocity per unit time. Mathematically -

a[avg] = Δv/Δt

Given in the question a sports car will accelerate from rest to a speed of 41.0 m/s in 7.20 s. From this, we can write -

Initial velocity [u] = 0 m/s

Final velocity [v] = 41 m/s

time taken (Δt) = 7.2 s

Part A → Average acceleration

The average acceleration of car can be calculated as follows -

a = Δv/Δt = (v - u)/t = (41 - 0) / 7.2 = 5.69 m/s²

Part B → Distance covered

The distance travelled by the car in first 7.20 seconds will be -

S = ut + 1/2 at²

S = 1/2 at²

S = 0.5 x 5.69 x 7.2 x 7.2

S = 147.5 m

Part C → Speed after 10 seconds

Using the first equation of motion -

v = u + at

v = at

v = 5.6 x 10

v = 56 m/s

Therefore, the magnitude of the average acceleration of the car is  5.69 m/s², the distance (in m) the car travels in the first 7.20 s is 147.5 m an the speed of the car (in m/s) 10.0 s after it begins its motion will be 56 m/s.

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The symbol of the element oxygen is O, its proton number is 8, its atomic mass is 16, its neutron number is 8 and finally; oxygen belong to period 2 of the periodic table.

That being said, every atom of an element has within its nucleus; proton and neutrons of which electrons revolve round it. In the case of oxygen, it has

Oxygen, because it belongs to group vi and period 2 of the periodic table has a valence electrons of 6 electrons. This means that oxygen is a non metals.

An element can simply be defined as a chemical substance which which cannot be split into simpler units by ordinary means

An atom is the smallest part of element which can take part in a chemical reaction. Oxygen is a diatomic element which means that it exist in its molecules consisting of two atoms.

Below are the names of some elements:

So therefore, the symbol of the element oxygen is O, its proton number is 8, its atomic mass is 16, its neutron number is 8 and finally; oxygen belong to period 2 of the periodic table.

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An electric field is defined along the x-axis by the function then if g=1.5m and h=6m, then v(g)-v(h) = 7768.40V.

When charge is present in any form, a point in space has an electric field that is connected to it.

The value of E, often known as the electric field strength, electric field intensity, or just the electric field, expresses the strength and direction of the electric field.

Each location in space where a charge exists in any form can be considered to have an electric field attached to it. The electric force per unit charge is another name for an electric field. The electric field’s equation is given as E = F / Q.

E = + 5 x^4 x^n

Also, E = -x^n r/rx (v)

⇒ 5 x^4 x^n = -x^n r/rx (v)

⇒ v = - ∫ 5 x^4 dx

⇒ v = -5 x^5/5

⇒ v = - x^5 v

So, v(g) - v(h) = - (1.5)^5 + (6)^5

= -7.59375 + 7776

=7768.40 V

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yes, it appears that births occur on the days of the week with frequencies that are about the same.

It is obvious from the relative frequency table that almost no day has a relative frequency value that is double that of any other day. We may thus draw the conclusion that these births happen almost equally frequently on each day of the week. Please keep in mind that the relative frequency statistics vary slightly over the course of seven days.

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The modulus of elasticity is 117.5 KN/[tex]cm^{2}[/tex].

How can we find the modulus of elasticity?

Modulus of elasticity is commonly known as Young's Modulus, which is denoted as E. To find modulus of elasticity we know that,

E = σ / ∈-----(1)

where σ is denoted as stress,

and   ∈ is denoted as strain.

σ  = F/A ------(2)

where F is denoted as load,

and A is denoted as area.

 ∈= ΔL/L ------(3)

where ΔL is denoted as the resulting change in length,

and L is denoted as the original length.

Given that,

L = 3.6m = 360cm

d = 2.6cm

F = 61 KN

ΔL = 3.52mm = 0.352cm

E = ?

By substituting the values in (2) & (3) we get,

  ⇒  σ  = F/A

  A =  π/4 [tex]d^{2}[/tex] = (π/4)×([tex]2.6^{2}[/tex]) = 5.3092 [tex]cm^{2}[/tex]

  σ = 61/(5.309) = 11.5

   ⇒ ∈ = ΔL / L

  = (0.352) / 360  

E = σ / ∈

  = [tex]\frac{(61)(360)}{(5.309)(0.352)}[/tex] = 1177 KN/[tex]cm^{2}[/tex]

Therefore the modulus of elasticity is 1177 KN/[tex]cm^{2}[/tex]

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Answer:

14.SI unit of

Distance →Metre(m)

Time →second(s)

Mass→kilogram(kg)

15. Dynamics

16. Optics

17. Electromagnetism

18.Thermodynamics

Answer:
14)
Distance : metres
Time: seconds
Mass: kilograms

15) Mechanics
16) Optics
17) Electromagnetism
18) Thermodynamics

Explanation:

Si units stand for 'International Units' these are units that are used universally for certain quantities

Hope this helps :)

By using Hooke's Law, the isentropic bulk modulus is 1,360,563.38 Pa.

We need to know about Hooke's Law to solve this problem. Hooke's Law describes the force applied to spring (elastic materials) will proportional to spring constant and displacement under the elastic condition. It can be described as

F = k . x

where F is force, k is spring constant and x is displacement.

The bulk modulus can be measured by stress and strain which

B = σ/ε

B = (F/A) / (ΔV/V)

where σ is stress, ε is strain, A is surface area, ΔV is change in volume and L is initial volume.

From the question above, we know that

σ = 276 kN/m² = 276 kPa = 276000 Pa

V = 0.35 m³

ΔV = 0.071 m³

By substituting the given parameters, we get

B = σ/ε

B = 276000 / (ΔV/V)

B = 276000 / (0.071/0.35)

B = 1,360,563.38 Pa

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Answer:

D. It is a non-metal.

The crest of an ocean wave moves a distance of given time is 2 m/s.

To know the speed of the wave,

Use the formula,

speed = distance / time

Given,

distance = 20 m

time = 10s

s = ?

Putting values,

s = d / t

s = 20 / 10

s = 2 m/s

Although some individuals may believe that average speed and average velocity are simply two different names for the same quantity, average speed depends on both distance and displacement. The average speed will be greater than the average velocity if an object changes direction while traveling.

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A chunk of metal gets burned through using an industrial laser. The RMS value of the electric field will be 2.25 mT.

Root Mean Square is the name for this phrase. The square root of the mean square of the voltage signal's instantaneous values is known as an RMS voltage. The quadratic mean is another name for the RMS. In terms of an integral of the squares of the instantaneous values over a cycle, RMS voltage can also be expressed as a continuously fluctuating voltage.

Average intensity of the light is S=1.21×[tex]10^{9}[/tex] w/m²

The RMS value will be :

S=ε₀c[tex](E_r_m_s)^{2}[/tex]

[tex](E_r_m_s)^{2}[/tex]=S/ε₀

=√(1.21×[tex]10^{9}[/tex]) / (8.85×[tex]10^{-12}[/tex])(3.0×[tex]10^{8}[/tex] m/s)

=6.75×[tex]10^{5}[/tex] N/c

B=[tex](E_r_m_s)[/tex]/c

=(6.75×[tex]10^{5}[/tex] N/c) / (2.25×[tex]10^{-3}[/tex] m/s)

=2.25×[tex]10^{-3}[/tex] T

=2.25 mT

Hence, the RMS value of the electric Field is 2.25 mT.

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Because Newton could not provide comprehensive proof, his Binomial Theorem is not a "theorem" in the sense of Euclid or Archimedes. Nonetheless, his knowledge and intuition served him well enough for him to construct a useful formula.

Furthermore, his intrinsic conviction in the persistence of patterns led him to believe that the formula that correctly generated coefficients for binomial powers such as (a+b)^2 or (a+b)^3 should also work for powers such as (a+b)^1/2 or (a+b)^−3.

Although Newton did not establish this finding, we do know how he came to it. Newton's explanation is offered in a pair of letters dated 1676 and delivered to Leibniz by Henry Oldenburg of the Royal Society. In it, he describes how he came to his conclusion in a roundabout way.

He was looking at the areas under the curves y=(1−x2)n2  from 0 to x for n=0, 1, 2, 3,.... These are simple to compute for even n. Newton was able to guess the solution for odd values of n by studying patterns and interpolating. Then he recognized that expressing (1−x2)n2 as an infinite series would provide the same results.

Newton wrote :

(P+PQ)mn=Pmn+mnAQ+m−n2nBQ+m−2n3nCQ+…

where P+PQ is the binomial to be considered; mn is the power to which the binomial will be raised "whether that power is integral or (so to speak) fractional, positive or negative"; and A,B,C,... indicate the term immediately preceding it in the expansion.

When compared to the present version, this may appear strange. When you remove the Pmn word from the right side and cancel, you get the more known form:

(1+Q)mn=1+mnQ+(m/n)(m/n−1)2Q2+(m/n)(m/n−1)(m/n−2)2×3Q3+(m/n)(m/n−1)(m/n−2)(m/n−3)2×3×4Q4+…

Thus, in Newton's notation,

A=Pmn

B=mnAQ=mnPmnQ

C=(m−n)2nBQ=(m−n)m(2n)nPmnQ2=(m/n)(m/n−1)2PmnQ^2

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As ice melts into water, kinetic energy is being added to the particles. This movement causes them to be 'excited' and causes the break in the bonds which hold them together as a solid. This also results in a change of state from solid to liquid.

kinetic energy can be described as a form of energy that an object or a particle possess by reason of its motion.

Kinetic energy is a property of a moving object or particle and that depends on the motion and mass of the object involved in the motion.

The change in state of an object is due to the change in the average kinetic energy of the particles. This average kinetic energy is proportional to the temperature of those particles.

The reason is that heat is a form of energy and if you add heat energy to ice you "excite" the water molecules which in turn breaks the interactions in the lattice structure and forming weaker, looser hydrogen-bonding interactions.

In conclusion, the change in state of an object is due to the change in the average kinetic energy of those particles.

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The arabinose operon in e. coli functions as the regulatory protein

The L-arabinose operon, commonly known as the ara operon, is a gene sequence that encodes enzymes required for arabinose catabolism to xylulose 5-phosphate, an intermediate in the pentose phosphate pathway. It is governed by both positive and negative control. Escherichia coli contains the operon (E. coli).

AraC, the regulator protein, is sensitive to arabinose levels and acts as both an activator in the presence of arabinose and a repressor in the absence of arabinose to regulate the expression of araBAD.

In the absence of arabinose, the dimer AraC protein represses the structural gene by binding to araI1 and araO2, and the DNA creates a loop, preventing RNA polymerase from connecting to the ara operon promoter and therefore stopping transcription. When arabinose is present, it binds to AraC, preventing it from interacting.

The DNA loop is therefore broken. AraC-arabinose complexes attach to the araI site, promoting transcription. When arabinose is present, AraC functions as an activator, resulting in the formation of a complex: AraC + arabinose. This complex is required for RNA polymerase to bind to the promoter and initiate transcription of the ara operon.

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An impartial explanation of water at a certain temperature has a concentration of oh- of 5.3 x 10^-7.

The kw at this temp = 2081 × [tex]10^{-13}[/tex]

It can also defined as solution is one which has an equal concentration of [tex]H^+[/tex] and [tex]OH^-[/tex] ions in the solution.

Hence,

Kw = 2081 × [tex]10^{-13}[/tex]

concentration  of   [tex]OH^{-}[/tex]= 5.3 ×  [tex]10^{-7}[/tex] M

For neutral solution  [tex]OH^{-}[/tex] = (H3O+) = 5.3 ×  [tex]10^{-7}[/tex] M

From relation from Kw,  [tex]OH^{-}[/tex], and H3O+

Kw = [ [tex]OH^{-}[/tex]][H3O+] =  5.3 ×  [tex]10^{-7}[/tex] M × 5.3 ×  [tex]10^{-7}[/tex] M

Kw = 2.81 ×  10_13

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