Erbium-165 has a half-life of 10.4 hours. If you start with 1,000 grams of
erbium-165, how much time will it take to have 125 grams of erbium-165 left
in the sample?
A. 41.6 hours
OB. 20.8 hours
C. 31.2 hours
D. 10.4 hours

The force of gravity on a 1–kilogram box located at a point from the center of Earth is 2.36 N

The force of attraction felt by a person at the center of a planet or Earth is called as the gravity.

Given, a 1 kg box located at a point 1.3 × 10⁷ m from the center of Earth. The Earth has the acceleration due to gravity, g =  9.81 m/s².

Force of gravity F = GMm/R²

where G = gravitational constant = 6.67 x 10⁻¹¹ N.m²/kg² and R is the distance between two masses.

The Mass of Earth M= 5.98 × 10²⁴ kg

Substituting the values, we get

F =  (6.67 x 10⁻¹¹ N.m²/kg² x 1kg x  5.98 × 10²⁴ kg)/ ( 1.3 × 10⁷ m)²

F = 2.36 N

Therefore,  the force of gravity on a 1–kilogram box located at a point from the center of Earth is 2.36 N

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The unit vector along r(t) will be 3t–4t^2+2

A vector is a quantity with direction and magnitude that is especially useful for locating one location in space in relation to another. A quantity or phenomena with independent qualities for both size and direction is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields weight are a few examples of vectors in nature.

Given the the position of particle as a function of particle of time is given by: r(t)=3tî–4t^2j+2k. Where î & j are unit vector along the x-axis and y-axis respectively.

We have to find the unit vector along r(t)

To find the unit vector along r(t) we have to put the value of (i,j,k) = (1,1,1) in r(t)

So,

r(t) = 3tî–4t^2j+2k

r(t) = 3t(1)–4t^2(1)+2(1)

r(t) = 3t–4t^2+2

Therefore the unit vector along r(t) will be 3t–4t^2+2

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By counting the number of crests that pass a point in a specific amount of time, one may determine the frequency of a waveform. Option a is correct.

A sound pressure wave's frequency, also known as pitch, is the number of times it repeats itself every second.

The frequency of the sound is the inverse of the period. If the wavelength of a wave is short. The wave will indeed have a lower frequency. A longer wavelength denotes a lower frequency.

The frequency of a waveform is found by determining the number of crests passing a point in a given time.

Hence option a is correct.

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The equivalent capacitance of these capacitors as they are arranged in series and parallel will be 0.093 μF and 71.1 μF.

A capacitor is a device that can store electrical energy. It is a two-conductor configuration separated by an insulating medium that carries charges of equal size and opposite sign.

If the capacitor is connected in the series the equivalent capacitance is found as;

[tex]\rm \frac{1}{c_{eq}} = \frac{1}{c_1} +\frac{1}{c_2} +\frac{1}{c_3} +\frac{1}{c_4} +\frac{1}{c_5} \\\\\ \rm \frac{1}{c_{eq}} = \frac{1}{10} +\frac{1}{50} +\frac{1}{9} +\frac{1}{2} +\frac{1}{0.1} \\\\\ \frac{1}{c_{eq}} = 0.1+0.02+0.11+0.5+10 \\\\ \frac{1}{c_{eq}} = 10.7 \\\\ c_{eq} = 0.093 \ \mu F[/tex]

If the capacitor is connected in parallel the equivalent capacitance,cₐ is found as;

cₐ= c₁+c₂+c₃+c₄+c₅

cₐ = 10+50+9+2+0.1 μF

cₐ =71.1 μF

Hence, the equivalent capacitance of these capacitors as they are arranged in series and parallel will be 0.093 μF and 71.1 μF.

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Answer:

Temperatures expressed in the Kelvin scale are D.) 273° higher than temperatures in the Celsius scale.

Explanation:

This answer is 110% correct guaranteed!

⭐⭐⭐⭐⭐ +

Answer:

Explanation:

If a positive charge is moving in the direction of electric field vector, its velocity will increase, whereas positive charge moving opposite to the direction of the electric of electric field will decelerate.

The case with a negative charge is just reversed verse, it will decelerate when moving along the field direction and accelerate when moving opposite to it.

(a) The sign of the unknown charge is negative.

(b) The magnitude of the unknown charge is 2.18 μC.

The charge is the physical quantity which defines the object's electric field. The charged objects creates the electric field around it and attracts or repels another objects coming into that field.

Given is a charged ball of mass m = 0.265 kg and unknown charge q is hanging by a light thread from a ceiling. A fixed charge Q = +5.00 μC on an insulated stand is brought close to the unknown charge. As a result, the unknown charge hangs at an angle 0 = 38.0° to the vertical as shown in the diagram below. The distance between the two charges is r = 22.0 cm.

Tension in the string has two components, Tsinθ and Tcosθ

(a) The fixed charge Q will attract the movable charge q attached to string. The charge Q is positive. So, the charges must of opposite sign.

Thus, the sign of unknown charge is negative.

(b) From the equilibrium of forces, we get

Electrostatic force Fe = kQq/r²

Fe =  Tsinθ .............(1)

and

weight force mg = Tcosθ.............(2)

Dividing both the equations, we get

mg/Fe = tanθ

mg / (kQq/r²) =  tanθ

q = mgr²tanθ / kQ

Substitute the values from the question, we have

q = 0.265 x 9.81 x (0.22)² tan38 / (9x10⁹ x 5 x 10⁻⁶)

q = 2.18 x 10⁻⁶ C

or q = 2.18 μC

Thus, the magnitude of charge is  2.18 μC.

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Answer:

eˣ-8.

Explanation:

(eˣ-8x+7)'=eˣ-8.

Plugging in a lamp is not an example of Static electricity. Thus, the correct option is C.

Static electricity may be defined as the consequence of an imbalance between negative and positive charges in an object. It does not involve the direct flow of electrons throughout a wire.

Clothes sticking together in the dryer and getting shocked when you touch a doorknob are examples of static electricity while plugging in a lamp is an example of mobile electricity that mediates the direct flow of electrons to generate an electric current and as a result, the lamp glows.

Therefore, the correct option for this question is C.

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D.

The gravitational of a body is possessed by the body due to the virtue of its position.

The formula for gravitational potential energy is,

                                P.E = mgh joules

Substituting the values

196*9.8*250= 49k

Answer:

shown below

Explanation:

2 x 10⁷ as a number is 20,000,000

20,000,000 - 10 = 19,999,990

It went 19,999,990 m/h

in km/h:

19,999,990 / 1000 = 19,999.99 km/h

in km/s

19,999,990 / 3,600,000 = ~5.56 km/s

in m/s

19,999,990 / 3600 = ~5555.56 m/s

1. The total mass of the rod is 61.48 kg.

2. The x-coordinate of the center of the mass for this rod is  172.6021 m.

The density is the ratio of the mass and the volume of the object. It is denoted by ρ.

ρ = mass/Volume = m/V

Given a long thin solid rod lies along the positive x-axis. One end is at x = 1.80 m and the other at x = 3.40 m. The linear mass density is

λ = ax³ + bx,

where λ is measured in kg/m, and the constants have the following values: a = 1.70 kg/m⁴ and b = 2.20 kg/m²

So, λ = 1.70x³ + 2.20x

1. The total mass of the rod is

m =₁.₈³⁴ ∫ [1.70x³ + 2.20x] dx

m = [ 1.70x⁴/4 + 2.20x² /2 ]₁.₈³⁴

Putting the limits, we have

m = 69.51 - 8.02548

m = 61.48 kg

Thus, the total mass of the rod is 61.48 kg

2. The x-coordinate of the center of the mass for this rod

Xcm =∫ xλdx/m

Xcm =∫[ x ( 1.70x³ + 2.20x) /m ]dx

Xcm =∫[( 1.70x⁴ + 2.20x²) /m ]dx

On integrating and putting the limits  x = 1.80 m to x = 3.40 m

Xcm = = [ {1.70(3.4)⁵/5 + 2.20(3.4)³ /3} - {1.70(1.8)⁵/5 + 2.20(1.8)³ /3} ]

Xcm = 183.3034 - 10.70133

Xcm = 172.6021 m

Thus,  the x-coordinate of the center of the mass for this rod is  172.6021 m.

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According to the pavlovian perspective, people who suffer from PTSD are classically conditioned.

This is referred to as post traumatic stress disorder which is a mental disorder from a terrifying incident.

The pavlovian perspective however view this disorder as being a type of classical conditioned one.

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The energy transformations in an electric motor are, electrical energy in current → changing magnetic field → mechanical energy. Option C is corect.

According to the law of conservation of energy, energy can neither be created nor destroyed, but it can be transferred from one form to another.

The total energy is the sum of all the energies present in the system. The potential energy in a system is due to its position in the system.

An electric motor is a mechanism that turns electricity into mechanical energy.

The interaction between the motor's magnetic field and electric current in a wire winding generates force in the form of torque imparted to the motor's shaft in most electric motors.

An electric generator is physically equivalent to an electric motor, but it converts mechanical energy into electrical energy using a reversed flow of power.

In an electric motor, energy is transformed into mechanical energy, electrical energy in current, and changing magnetic energy.

The energy transformations in an electric motor are;

Electrical energy in current → changing magnetic field → mechanical energy.

Hence option C is correct.

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Answer:

1 W

Explanation:

Power is the ratio of the total work done by the body to the time it will takes to do the work.

Total Work done = Potential energy (P.E) = mgh

Total work done = mgh

Total work done = 1kg × 10m/s² × 1m

Total work done = 10 J

Therefore Total Work done is 10J.

And then time is 10 s.

Power = Total Work done divided by time

Power = 10 J÷ 10 s = 1 W

there is no pic or whatever to show

Answer:

8.4335 x 10^-²¹, 1.78204 x 10²⁶

Explanation:

p = mv

p = (5.05 x 10⁶)(1.67 x 10^-²⁷)

p = 8.4335 x 10^-²¹

p = mv

p = (5.98 x 10²⁴)(2.98 x 10)

p = 1.78204 x 10²⁶

Answer:

You are correct, the answer is capacitor

Answer:

it is much more efficient than any other process to generate power

The work done is positive and is equal to 20000 J

Work done is defined as the product of force and the distance moved by the force.

Mathematically:

The work done by the force = 20 * 1000 = 20000J

The work done is positive and is equal to 20000 J

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(a) The work done in moving the unit charge from point C to A is 7.62 x 10⁻³ J.

(b) The work done in moving the unit charge from point D to B is 7.62 x 10⁻³ J.

W = Fd

W = Kq²/d

W(C to A) = W(0 to C) + W(0 to A)

[tex]W(C \ to \ A) = - \frac{Kq^2}{7.07} + \frac{Kq^2}{5} \\\\ W(C \ to \ A) = 0.0586 \ Kq^2\\\\W(C \ to \ A) = 0.0586 \times 9 \times 10^9 \times (3.8\times 10^{-6})^2\\\\W(C \ to \ A) = 7.62 \times 10^{-3} \ J[/tex]

W(D to B) = W(0 to D) + W(0 to B)

W(D to B) = 7.62 x 10⁻³ J

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The voltage of the secondary will be 36 V.From the given conditions primary transformer has 3 times as many turns in the secondary coil.

Electromagnetic induction is what causes the induced voltage. Electromagnetic induction is the process of generating emf (induced voltage) by subjecting a conductor to a magnetic field.

In this case, a magnet is pushed in and out of a wire coil attached to a high-resistance voltmeter.

Typically, a transformer's primary winding is attached to the input voltage source and changes electrical power into a magnetic field.

The secondary winding's role is to turn this alternating magnetic field into electricity, generating the necessary output voltage.

Given data;

Primary coil voltage,[tex]\rm V_P = 12 \ v[/tex]

Secondary coil voltage,[tex]\rm V_s = ?[/tex]

No turns in the primary coil,[tex]\rm N_p[/tex]

No turns in the secondary coil,[tex]\rm N_s[/tex]

From the given condition;

[tex]\rm N_s = 3N_p[/tex]

For a transformer,

[tex]\rm \frac{V_p}{V_s}= \frac{N_p}{N_s} \\\\ \rm \frac{12}{V_s}= \frac{N_p.}{3N_p} \\\\ V_s = 36 \ V[/tex]

Hence the voltage of the secondary will be 36 V.

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Answer:  Solar Photovoltaic (PV) cells generate electricity by absorbing sunlight and using that light energy to create an electrical current. There are many PV cells within a single solar panel, and the current created by all of the cells together adds up to enough electricity to help power your school, home and businesses.

                              --Cited from Solar Schools

The internal energy of the gas after the adiabatic compression will be 30.398 × 10⁶ J

When energy is moved from one store to another, work is completed. Work done on the gas is taken as -ve.

Given data;

pressure(P)=3.0 atm = 303975 N/m²

The initial volume, V₁

work is done on the gas., W=?(-ve)

Change in heat, ΔQ=0

Change in the internal energy of the gas., ΔE

The work done on the gas;

W = -PΔV

W= - 303975 N/m² × 100 cm³

W = - 30.3 × 10⁶ J

The internal energy is found as;

ΔE=q+w

ΔE= 0-30.3 × 10⁶ J

ΔE= -30.3 × 10⁶ J

E₂-E₁= -30.3 × 10⁶ J

E₂ = -30.3  × 10⁶ J +500

E₂ = 30.398 × 10⁶ J

Hence, the internal energy of the gas after the adiabatic compression will be 30.398 × 10⁶ J

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The answer to the first part of the question is 24 V and the answer to the second part of the question is 48 V.

The formula which relates Charge, Capacitance and Voltage is

Charge = Capacitance × Voltage

Q = CV

where Q denotes the charge, C denotes the capacitance and V denote the voltage.

Using the above formula the charge on the capacitance will be

Q = CV

C = 10 mF

V = 24 V

Q = 240 mC

Charge on capacitance is 240 mC.

Now after we disconnect the battery

C = 10 mF (will remain same)

Q = 240 mC

V = Q/C

V = 240/10 V

V = 24 V

So after we removed the battery, The voltage will remain same.

Now we know that parallel plate capacitor formula is

C = ε(A/d)

from here

C ∝ 1/d, and as there is no loss of charge we can say that V ∝ 1/d

Form C ∝ 1/d and V ∝ 1/C we can state that

V ∝ d   {where d is the measurement of separation between the plates}

so if we double the distance between the plates then, the voltage will also get double.

Previously our voltage was 24 V, now if we double the distance between the plates the voltage will also get double, and it will become 48 V.

So, the voltmeter will take a reading of 24 V if voltmeter is connected across the two plates without discharging them, and if we double the plate separation then it will take 48 V as reading.

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Considering the Watt's law, if a current uses 31 amperes and has a voltage of 110 volts, it dissipates 3,410 Watts.

Current is the physical magnitude that expresses the amount of electricity that flows through a conductor in unit time and is measured in amps.

The voltage is the difference between the electrical charge that leaves the source and the one that finally reaches the end of the circuit. It is expressed in volts.

Watt's Law refers to the electrical power of an electronic component or device and is defined as the power consumed by the load is directly proportional to the voltage supplied and the current flowing through it. The unit of power is the Watt.

Knowing the voltage and current, this law is expressed as:

P = V×I

In this case, you know:

Replacing in Watt's Law:

P = 110 volts× 31 amperes

Solving:

P= 3,410 Watt

Finally, if a current uses 31 amperes and has a voltage of 110 volts, it dissipates 3,410 Watts.

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