Answer:
Explanation:
Let the charge on proton be q .
energy gain by proton in a field having potential difference of V₀
= V₀ q
Due to gain of energy , its kinetic energy becomes 1/2 m v₀²
where m is mass and v₀ is velocity of proton
V₀ q = 1/2 m v₀²
In the second case , gain of energy in electrical field
= 2 V₀q , if v be the velocity gained in the second case
2 V₀q = 1/2 m v²
1/2 m v² = 2 V₀q = 2 x 1/2 m v₀²
mv² = 2 m v₀²
v = √2 v₀
A very fine thread is placed between two glass plates on one side and the other side is touching to form a wedge. A beam of monochromatic light of wavelength 600 nm illuminates the wedge and 178 bright fringes are observed. What is the thickness of the thread?
Answer:
53.3micro meters
Explanation:
See attached file
An electromagnetic standing wave in air of frequency 750 MHz is set up between two conducting planes 80.0 cm apart. At how many positions between the planes could a point charge be placed at rest so that it would remain at rest?
Answer:
The positions the point charge will be placed at rest and still remain at rest are 20 cm, 40 cm, and 60 cm between the ends.
Explanation:
Given;
distance between the conducting planes, d = 80 cm
frequency of the electromagnetic wave, f = 750 MHz
speed of light, c = 3 x 10⁸ m/s²
Determine the wavelength
λ = C/f
where;
λ is the wavelength
C is the speed of light
f is the frequency
λ = C/f
λ = (3 x 10⁸) / (750 x 10⁶)
λ = 0.4 m = 40 cm
One complete cycle = one wavelength = 40 cm
half of the wavelength ( λ / 2) = 20 cm
one wavelength + half wavelength (3λ / 2) = 60 cm
The positions of the wave at zero amplitude (between 0 and 80 cm) = 20 cm, 40 cm, 60 cm
Thus, the positions the point charge will be placed at rest and still remain at rest are 20 cm, 40 cm, and 60 cm between the ends.
How would the interference pattern produced by a diffraction grating change if the laser light changed from red to blue?
Answer
fringe separation l distance between maxima decreases
Explanation:
Because the wavelength of blue light is smaller than that if red light
A balloon is ascending at a rate of +4.00 m/s to a height of 11.0 m above the ground when a package is dropped. In the absence of air resistance, the velocity of the ball when it hits the ground is
Answer:
Vf = 14.7 m/s
Explanation:
Vf² = Vi² + 2 * a * Δy
given:
a = 9.81 m/s²
Δy = 11m
Vi = 0 when upon release
Vf² = 0 + 2 (9.81) 11
Vf = 14.7 m/s
The velocity of the ball when it hits the ground will be 14.7 m/s.
What is velocity?The change of displacement with respect to time is defined as the velocity. Velocity is a vector quantity. it is a time-based component. Velocity at any angle is resolved to get its component of x and y-direction.
given:
a(gravitational acceleration) = 9.81 m/s²
s (distance)= 11m
v is final velocity
u is the initial velocity
From Newton's second equation of motion;
[tex]\rm v^2 = u^2+2as \\\\ v^2=2 \times 9.81 \times 11 \\\\ v= 14.7 \ m/sec[/tex]
Hence, the velocity of the ball when it hits the ground will be 14.7 m/s.
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What is the change in internal energy of the system (∆U) in a process in which 10 kJ of heat energy is absorbed by the system and 70 kJ of work is done by the system?
Answer:
Explanation:
According to first law of thermodynamics:
∆U= q + w
= 10kj+(-70kJ)
-60kJ
, w = + 70 kJ
(work done on the system is positive)
q = -10kJ ( heat is given out, so negative)
∆U = -10 + (+70) = +60 kJ
Thus, the internal energy of the system decreases by 60 kJ.
If a 950 kg merry-go-round platform of radius 4.5 meters is driven by a mechanism located 2.0 meters from its center of rotation, how much force must the mechanism provide to get the platform moving at 5.5 revolutions per minute after 12 seconds if it were initially at rest
Answer:
F = 213.75 N
Explanation:
First we need to calculate the angular acceleration of merry-go-round. For that purpose we use 1st equation of motion in angular form.
ωf = ωi + αt
where,
ωf=final angular velocity=(5.5 rev/min)(2π rad/1 rev)(1 min/60 s)=0.58 rad/s
ωi =initial angular velocity = 0 rad/s
t = time = 12 s
α = angular acceleration = ?
Therefore,
0.58 rad/s = 0 rad/s + α(12 s)
α = (0.58 rad/s)/(12 s)
α = 0.05 rad/s²
Now, we shall find the linear acceleration of the merry-go-round:
a = rα
where,
a = linear acceleration = ?
r = radius = 4.5 m
Therefore,
a = (4.5 m)(0.05 rad/s²)
a = 0.225 m/s²
Now, the force is given by Newton;s 2nd Law:
F = ma
where,
F = Force = ?
m = mass pf merry-go-round = 950 kg
Therefore,
F = (950 kg)(0.225 m/s²)
F = 213.75 N
A capacitor that is initially uncharged is connected in series with a resistor and an emf source with E=110V and negligible internal resistance. Just after the circuit is completed, the current trhough the resistor is 6.5*10^-5A. the time constant for the circuit is 4.8s.
1) What is the resistance of the resistor?
2) What is the capacitance of the capacitor?
Answer:
1
[tex]R = 1.692*10^{6} \Omega[/tex]
2
[tex]C = 2.837 *10^{-6} \ F[/tex]
Explanation:
From the question we are told that
The voltage is [tex]E = 110 \ V[/tex]
The current is [tex]I = 6.5 *10^{-5} \ A[/tex]
The time constant is [tex]\tau = 4.8 \ s[/tex]
The resistance of resistor is mathematically evaluated as
[tex]R = \frac{E}{I}[/tex]
substituting values
[tex]R = \frac{ 110 }{ 6.5*10^{-5}}[/tex]
[tex]R = 1.692*10^{6} \Omega[/tex]
The capacitance of the capacitor is mathematically represented as
[tex]C = \frac{\tau}{R}[/tex]
substituting values
[tex]C = \frac{ 4.8}{ 1.692*10^{6}}[/tex]
[tex]C = 2.837 *10^{-6} \ F[/tex]
If you were to calculate the pull of the Sun on the Earth and the pull of the Moon on the Earth, you would undoubtedly find that the Sun's pull is much stronger than that of the Moon, yet the Moon's pull is the primary cause of tides on the Earth. Tides exist because of the difference in the gravitational pull of a body (Sun or Moon) on opposite sides of the Earth. Even though the Sun's pull is stronger, the difference between the pull on the near and far sides is greater for the Moon.
Required:
a. "Let F(r) be the gravitational force exerted on one mass by a second mass a distance r away. Calculate dF(r)/dr to show how F changes as r is changed.
b. Evaluate this expression for dF(r) jdr for the force of the Sun at the Earth's center and for the Moon at the Earth's center.
c. Suppose the Earth-Moon distance remains the same, but the Earth is moved closer to the Sun. Is there any point where dF(r)/dr for the two forces has the same value?
Answer:effective
Explanation:
A skater of mass 45.0 kg standing on ice throws a stone of mass 7.65 kg with a speed of 20.9 m/s in a horizontal direction. Find:
a. The speed of the skater after throwing the stone.
b. The distance over which the skater will move in the opposite direction if the coefficient of kinetic friction between his skates and the ice is 0.03.
Answer:
Explanation:
know that there is no external force on skater and the stone so the total momentum of the system will remains constant
so we will have
here we have
so the skater will move back with above speed
now the deceleration of the skater is due to friction given as
Answer:
(a) 3.553 m/s
(b) 21.46 m
Explanation:
(a) Applying the law of of momentum,
Total momentum before collision = Total momentum after collision
mu+m'u' = mv+m'v'.................. Equation 1
Where m and m' are the mass of skater and stone respectively, u and u' are the initial velocity of skater and stone respectively, v and v' are the final velocity of the skater and the stone respectively.
Note, u = 0 m/s, u' = 0 m/s
Therefore,
0 = mv+m'v'
-mv = m'v'................ Equation 2
make v the subject of the equation
v = -m'v'/m............. Equation 3
Given: m = 45 kg, m' = 7.65 kg, v' = 20.9 m/s
Substitute into equation 3
v = 7.65(20.9)/45
v = -3.553 m/s
Hence the speed of the skater = 3.553 m/s
(b) F = mgμ..............Equation 4
But F = ma
Therefore,
ma = mgμ
a = gμ............... Equation 5
Where a = acceleration of the skater, g = acceleration due to gravity, μ = coefficient of kinetic friction
Given: μ = 0.03, g = 9.8 m/s²
Substitute into equation 5
a = 0.03(9.8)
a = 0.294 m/s²
Using the equation of motion,
v² = u²+2as............. Equation 6
Where s = distance moved by the skater.
note that u = 0 m/s.
therefore,
v² = 2as
s = v²/2a................ Equation 7
Given: v = 3.553 m/s, a = 0.294
Substitute into equation 7
s = 3.553²/(2×0.294)
s = 12.62/0.588
s = 21.46 m
Use I=∫r2 dm to calculate I of a slender uniform rod of length L, about an axis at one end perpendicular to the rod. note: a "slender rod" often refers to a rod of neglible cross sectional area, so that the volume is the Length, and the mass density X Length.
Answer:
The moment of inertia of a slender uniform rod of length L about an axis at one end perpendicular to the rod is [tex]I = \frac{1}{3}\cdot m \cdot L^{2}[/tex].
Explanation:
Let be an uniform rod of length L whose origin is located at one one end and axis is perpendicular to the rod, such that:
[tex]\lambda = \frac{dm}{dr}[/tex]
Where:
[tex]\lambda[/tex] - Linear density, measured in kilograms per meter.
[tex]m[/tex] - Mass of the rod, measured in kilograms.
[tex]r[/tex] - Distance of a point of the rod with respect to origin.
Mass differential can translated as:
[tex]dm = \lambda \cdot dr[/tex]
The equation of the moment of inertia is represented by the integral below:
[tex]I = \int\limits^{L}_{0} {r^{2}} \, dm[/tex]
[tex]I = \lambda \int\limits^{L}_{0} {r^{2}} \, dr[/tex]
[tex]I = \lambda \cdot \left(\frac{1}{3}\cdot L^{3} \right)[/tex]
[tex]I = \frac{1}{3}\cdot m \cdot L^{2}[/tex] (as [tex]m = \lambda \cdot L[/tex])
The moment of inertia of a slender uniform rod of length L about an axis at one end perpendicular to the rod is [tex]I = \frac{1}{3}\cdot m \cdot L^{2}[/tex].
The _____________ is the thermonuclear fusion of hydrogen to form helium operating in the cores of massive stars on the main sequence
What is the only force that acts on an object in free fall? centripetal friction gravity
Answer:
one with only gravity acting upon it
Explanation:
Edgenuity :)
An object has an acceleration of 6.0 m/s/s. If the net force was tripled and the mass were doubled, then the new acceleration would be _____ m/s/s.
Answer:
The new acceleration would be 9 m/s².
Explanation:
Acceleration of an object is 6 m/s²
Net force is equal to the product of mass and acceleration i.e.
F = ma
[tex]a=\dfrac{F}{m}\\\\\dfrac{F}{m}=6\ m/s^2[/tex]
If the net force was tripled and the mass were doubled, it means,
F' = 3F
m' = 2m
Let a' is new acceleration. So,
[tex]a'=\dfrac{F'}{m'}\\\\a'=\dfrac{(3F)}{(2m)}\\\\a'=\dfrac{3}{2}\times \dfrac{F}{m}\\\\a'=\dfrac{3}{2}\times 6\\\\a'=9\ m/s^2[/tex]
So, the new acceleration would be 9 m/s².
The index of refraction of a certain material is 1.25. If I send red light (700 nm) through the material, what will the frequency of the light be in the material
Answer:
f1 / f2 = n2 / n1
Explanation:
To solve this problem, we should remember that the formula for index of refraction is defined as:
n = c / v
or
n v = c
Where,
n = index of refraction
c = speed of light
v = speed of light in the medium
Since speed of light is constant, then we can simply equate the materials 1 and 2:
n1 v1 = n2 v2
Where the speed of light in the medium (v) can be expressed as:
v = w * f
Where,
w = wavelength of light
f = frequency of light
Therefore substituting this back into the relating equation:
n1 w1 f1 = n1 w2 f1
Since it is given that the light is monochromatic, w1 = w2, this further simplifies the equation to:
n1 f1 = n2 f2
f1 / f2 = n2 / n1 (ANSWER)
A spaceship is moving past Earth at 0.99c. The spaceship fires two lasers. Laser A is in the same direction it is traveling, and Laser B is in the opposite direction. How fast will the light from each laser be traveling according to an observer on Earth?
Answer:
Vx' = (Vx - u) / (1 - Vx *u / c^2) velocity transformation formula
In both cases we wish to measure the velocity in the frame of the earth which is moving at speed u = -.99 c relative to the spaceship
VA' = (c + .99c) / (1 - (-.99 c * c) / c^2) = 1.99c / 1.99 = c
VB' = (-c + .99c) / (1 - (-c * -.99c) / c^2) = .01 c / .01 = c
In both cases an observer on earth will observe the light traveling at speed c.
A 20 kg child is on a swing that hangs from 2.6-m-long chains. What is her maximum speed if she swings out to a 46 angle?
Answer:
Explanation:
Here potential energy lost = mgh
h = L ( 1 - cos 46 ) where L is length of rope
= 2.6 x ( 1 - cos 46 )
PE lost = 20 x 9.8 x 2.6 ( 1 - cos 46 )
= 155.6 J
gain of kinetic energy = loss of PE
1/2 m v² = 155.6
.5 x 20 x v² = 155.6
v² = 15.56
v = 3.94 m /s
The magnitude of the Poynting vector of a planar electromagnetic wave has an average value of 0.939 W/m2. The wave is incident upon a rectangular area, 1.5 m by 2.0 m, at right angles. How much total electromagnetic energy falls on the area during 1.0 minute
Answer:
The total energy is [tex]T = 169.02 \ J[/tex]
Explanation:
From the question we are told that
The Poynting vector (energy flux ) is [tex]k = 0.939 \ W/m^2[/tex]
The length of the rectangle is [tex]l = 1.5 \ m[/tex]
The width of the rectangle is [tex]w = 2.0 \ m[/tex]
The time taken is [tex]t = 1 \ minute = 60 \ s[/tex]
The total electromagnetic energy falls on the area is mathematically represented as
[tex]T = k * A * t[/tex]
Where A is the area of the rectangle which is mathematically represented as
[tex]A= l * w[/tex]
substituting values
[tex]A= 2 * 1.5[/tex]
[tex]A= 3 \ m^2[/tex]
substituting values
[tex]T = 0.939 * 3 * 60[/tex]
[tex]T = 169.02 \ J[/tex]
In your words, describe how momentum is related to energy.
Answer:
you need momentum in order to release energy. For example, if you need to push something heavy and you get a running head start, then it will be easier.
Explanation:
A body's current radiation rate is 30% higher than it was an hour ago. Calculate the percentage by which your temperature increased.
Answer:
6.8%
Explanation:
According to Stefan-Boltzmann law, radiation is directly proportional with temperature raised to the fourth power:
P ∝ T⁴
Writing a proportion:
P₁ / P₂ = T₁⁴ / T₂⁴
1.3P / P = (T₁ / T₂)⁴
T₁ / T₂ = ∜1.3
T₁ = 1.068 T₂
The temperature increased by 6.8%.
2. A wire 4.00 m long and 6.00 mm in diameter has a resistance of 15.0 mΩ. A potential difference of 23.0 V is applied between the end. a) What is the current in the wire? b) Calculate the resistivity of the wire material. c) Try to identify the material.
Answer:
Explanation:
a )
current in the wire = potential diff / resistance
= 23 / (15 x 10⁻³ )
= 1.533 x 10³ A .
b )
For resistance of a wire , the formula is
R = ρ L / S where ρ is specific resistance , L is length and S is cross sectional area of wire
putting the given values
15 x 10⁻³ = 4ρ / π x .003²
ρ = 106 x 10⁻⁹ ohm. m
= 10.6 x 10⁻⁸ ohm m
The metal wire appears to be platinum .
(a) The current in the wire is 1.533 x 10³ A
(b) The resistivity of the wire material is 10.6 x 10⁻⁸ Ωm
(c) The material of the wire is Platinum
Ohm's Law and resistivity:
(a) According to the Ohm's Law:
V = IR
where V is the potential difference
I is the current
and R is the resistance
So,
I = V/R
I = 23 / (15 x 10⁻³ )
I = 1.533 x 10³ A
(b) The resistance of a wire is expressed as:
R = ρ L / A
where ρ is the resistivity,
L is length
and A is the cross-sectional area
15 x 10⁻³ = 4ρ / π x .003²
ρ = 106 x 10⁻⁹ Ωm
ρ = 10.6 x 10⁻⁸ Ωm
The metal from which the wire is made is platinum.
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A 25 kg box sliding to the left across a horizontal surface is brought to a halt in a distance of 15 cm by a horizontal rope pulling to the right with 15 N tension.
Required:
a. How much work is done by the tension?
b. How much work is done by gravity?
The work done by tensional force of the rope is 2.25 J and the work done by gravity is 36.75 J.
The given parameters;
mass of the box, m = 25 kgdistance traveled by the box, d = 15 cm = 0.15 mtension on the rope, T = 15 NThe work done by the tension is calculated as follows;
W = Fd
W = 15 x 0.15
W = 2.25 J
The work done by gravity is calculated as;
W = (25 x 9.8) x 0.15
W = 36.75 J
Thus, the work done by tensional force of the rope is 2.25 J and the work done by gravity is 36.75 J.
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Tesla Model S and the driver have a total mass of 2250 kg. The projected front area of the car is 2.35 m2. The car is traveling at 72km/hr when the driver puts the transmission into neutral and allows the car to freely coast until after 105 seconds its speed reaches 54 km/hr. Determine the drag coefficient for the car, assuming its values is constant. Neglect rolling and other mechanical resistance.
Answer:
The drag coefficient of the car is 0.189
Explanation:
mass of the car = 2250 kg
Frontal area of the car = 2.35 m^2
initial speed of the car = 72 km/hr = (72 x 1000)/3600 = 20 m/s
final speed of the car = 54 km/hr = (54 x 1000)/3600 = 15 m/s
time taken by the car to slow down = 105 sec
We'll assume that the value of the drag coefficient is constant throughout the deceleration.
The car decelerates from 20 m/s to 15 m/s in 105 seconds, the deceleration is calculated from
[tex]a = \frac{v-u}{t}[/tex]
where a is the deceleration
v is the final speed of the car
u is the initial speed of the car
t is the time taken to decelerate.
imputing values, we'll have
[tex]a = \frac{15-20}{105}[/tex] = -0.0476 m/s^2 (the -ve sign indicates a deceleration, which is a negative acceleration)
we can safely ignore the -ve sign in other calculations that follows
The force (drag force) with which the air around the decelerates the car is equal to..
[tex]F_{D} = ma[/tex]
where [tex]F_{D}[/tex] is the drag force
m is the mass of the car
a is the deceleration of the car
imputing values, we'll have
[tex]F_{D} = 2250*0.0476[/tex] = 107.1 N
equation for drag force is
[tex]F_{D} = \frac{1}{2}pAC_{D} v^{2}[/tex]
where p is the air density ≅ 1.225 kg/m³
A is the frontal area of the car
[tex]C_{D}[/tex] is drag coefficient of the car
v is the relative velocity of air and the car, and will be taken as the initial velocity of the car before starting to decelerate.
imputing these values, we'll have
[tex]107.1 = \frac{1}{2}*1.225*2.35*C_{D}*20^{2}[/tex] = 575.75[tex]C_{D}[/tex]
[tex]C_{D}[/tex] = 107.1/575.75 = 0.189
Huygens claimed that near the surface of the Earth the velocity downwards of an object released from rest, vy, was directly proportional to the square root of the distance it had fallen, . This is true if c is equal to
Answer:
the expression is False
Explanation:
From the kinematics equations we can find the speed of a body in a clean fall
v = v₀ - g t
v² = V₀² - 2 g y
If the body starts from rest, the initial speed is zero (vo = 0)
v= √ (2g y)
In the first equation it gives us the relationship between speed and time.
With the second equation we can find the speed in which the distance works, this is the expression, see that speed is promotional at the height of a delicate body.
Therefore the expression is False
if F, V, and we're chosen as fundamental unit of force, velocity and time respectively , the dimensions of mass would be represented as
Answer:
The dimension of mass can be represented as: [tex][F^{1} T^{1} V^{-1} ][/tex]
Explanation:
We have Force = Mass X Acceleration
= Mass X [tex]\frac{Change in Velocity}{Time Taken}[/tex]
or, Mass = Force x [tex]\frac {Time Taken } { Change in Velocity }[/tex]
So, dimensions of mass = [tex]\frac{[F][T]}{[V]}[/tex]
= [tex][F^{1} T^{1} V^{-1} ][/tex]
Rank the electromagnetic radiation from lowest to highest in the simulation in terms of energy, wavelength, and frequency.
a. Energy
b. Wavelength
c. Frequency
Answer:
A.ENERGY: Radio<microwaves<infrared<visible light<ultraviolet<xrays<gammarays
B. WAVELENGTH: Radio>microwaves> infrared>visible light>ultraviolet>xray> gammarays
C. FREQUENCY: Radio<microwaves<infrared<visible light<ultraviolet<xray< gammarays
Explanation:
THIS IS BECAUSE OF THE FOLLOWING EQUATIONS
1.ENERGY (E)= hX freqency
So as energy of radiation increases frequency also increases
2. Velocity (v) = wavelength x frequency
So as wavelength increases frequency decreases and vice versa
dandre expands 120w of power in moving a couch 15 meters in 5 seconds how much force does he exert ?
Answer:
The answer is 40 N for APX
Explanation:
A cylindrical coil of radius 6 cm is placed in magnetic field, which is changing in time with the rate 0.5 T/s. The magnetic field direction is parallel to the cylinder axis. What should be the number of turns in the coil to induce the emf
induced emf value is missing..
please correct the question
Rick spends four hours researching on the internet and does 1090 J of work. In the process, his internal energy decreases by 2190 J. Determine the value of Q, including the algebraic sign.
Answer:
Q = -3280J
Explanation:
From the First Law of Thermodynamics, energy cannot be created nor destroyed but it can be converted from one form to another with the interaction of heat. Mathematically, this can be expressed as:
ΔU = Q + W ----------(i)
Where;
ΔU = total change in internal energy of a system.
Q = heat exchanged between the system and the surrounding
W = work done by or on the system.
If heat is lost into the surrounding, then Q = -ve, else Q = +ve
If work is done on the system, then W = -ve, else W = -ve
=> From the question, Rick is the system and does a work of
W = +1090J [since Rick does the work, W = +ve]
=>Also, the internal energy decreases by 2190J, therefore,
ΔU = -2190J [since there is a decrease in internal energy]
Substitute the values of W and ΔU into equation (i) as follows;
-2190 = Q + 1090
=> Q = -2190 - 1090
=> Q = -3280J
Therefore, the value of Q = -3280J
Do women like when men shave their pubic hair?
Answer:
Maybe
Explanation:
Tbh it’s different for every women. Most women would say yes because having a bush is a bit disturbing for some and/or could be in return for a women shaving down there (if they do)
The free-electron density in a copper wire is 8.5×1028 electrons/m3. The electric field in the wire is 0.0520 N/C and the temperature of the wire is 20.0∘C. Use the resistivity at room temperature for copper is rho = 1.72×10^−8 Ω⋅m.
Required:
a. What is the drift speed vdvd of the electrons in the wire?
b. What is the potential difference between two points in the wire that are separated by 25.0 cm?
(a) The drift speed of electrons in the wire is 2.22 x 10⁻⁴ m/s.
(b) The potential difference between two points in the wire is 0.013 V.
The given parameters;
electron density of the copper wire, n = 8.5 x 10²⁸ electrons/m³.electric field, E = 0.0520 N/Ctemperature of the wire, t = 20 ⁰Cresistivity of the copper wire, ρ = 1.72 x 10⁻⁸ Ω⋅mThe drift speed of electrons in the wire is calculated as follows;
[tex]v_d = \frac{I}{qn A} \\\\but , \ \frac{I}{A} = \frac{E}{\rho} \\\\v_d = \frac{E}{qn \rho}[/tex]
where;
E is the electric fieldq is charge of electron = 1.602 x 10⁻¹⁹ C[tex]v_d = \frac{0.052}{1.602 \times 10^{-19} \times 8.5\times 10^{28} \times 1.72 \times 10^{-8}} \\\\v_d = 2.22 \times 10^{-4} \ m/s[/tex]
The potential difference between two points in the wire, separated by 25 cm;
V = Ed
where;
d is the distance of separation = 25 cm = 0.25 mV = 0.052 x 0.25
V = 0.013 V
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