A)<span>
dQ = ρ(r) * A * dr = ρ0(1 - r/R) (4πr²)dr = 4π * ρ0(r² -
r³/R) dr
which when integrated from 0 to r is
total charge = 4π * ρ0 (r³/3 + r^4/(4R))
and when r = R our total charge is
total charge = 4π*ρ0(R³/3 + R³/4) = 4π*ρ0*R³/12 = π*ρ0*R³ / 3
and after substituting ρ0 = 3Q / πR³ we have
total charge = Q ◄
B) E = kQ/d²
since the distribution is symmetric spherically
C) dE = k*dq/r² = k*4π*ρ0(r² - r³/R)dr / r² = k*4π*ρ0(1 -
r/R)dr
so
E(r) = k*4π*ρ0*(r - r²/(2R)) from zero to r is
and after substituting for ρ0 is
E(r) = k*4π*3Q(r - r²/(2R)) / πR³ = 12kQ(r/R³ - r²/(2R^4))
which could be expressed other ways.
D) dE/dr = 0 = 12kQ(1/R³ - r/R^4) means that
r = R for a min/max (and we know it's a max since r = 0 is a
min).
<span>E) E = 12kQ(R/R³ - R²/(2R^4)) = 12kQ / 2R² = 6kQ / R² </span></span>
The boundary between the crust and mantle is marked by a seismic-velocity discontinuity is called Mohorovicic discontinuity.
Mohorovicic discontinuity was discovered by Andrija Mohorovicic in 1909 who was a Croatian seismologist. He realized that the velocity of a seismic wave is related to the material's density where it is moving through. He decoded that the acceleration of the seismic waves that are observed within outer shell of the earth is a compositional change. Thus, the acceleration should be caused by a material of higher density.
Answer:
k = 1.30
Explanation:
For this exercise let's write the capacitance in air and with dielectric
air C₀ = Q / DV
dielectric C = k Q / DV
They tell us that the capacitor is charged and then the battery is disconnected, therefore the charge stored on the plate remains constant.
therefore the capacitance a changes to the value
C = k C₀
The voltage in the presence of dielectric must meet the relationship
ΔV = ΔV₀ / k
k = ΔV₀ /ΔV
let's calculate
k = 60/46
k = 1.30
Answer:
Two factors effecting the magnitude of the force of gravity between 2 objects are the product of their masses and square of distance between them.
Explanation:
According to Newton's law of universal gravitation
where F is the gravitational force, G is the universal gravitational constant and its value is 6.6743 × 10⁻¹¹ Nm²/kg₂ , m₁ and m₂ are masses of bodies and r is the distance between them.
It can be seen from the above equation that F is directly proportional to the product of the masses and inversely proportional to the square of distance between them.
F ∝ m₁m₂
F ∝ 1/r²
As far as the masses of the bodies increase, magnitude of the Gravitational force increases and if distance between them increase then Gravitational force between them decreases.
Answer:
2.46 eV
Explanation:
It is given that,
The energy of light that fall on the metal = 3.56 eV
The stopping potential of the metal = 1.1 V
We need to find the work function of the metal. It is given by the relation as follows :
W = E-KE ...(1)
Where KE is the kinetic energy of the ejected electron and it is given by :
KE = V×e
= 1.1 eV
Put all the values in formula (1)
W = 3.56 eV - 1.1 eV
= 2.46 eV
Hence, the work function of the metal is 2.46 eV. Hence, the correct option is (c).
