Answer:
Explanation:
The final angle speed of the merry-go-round is determined with the help of the Principle of Angular Momentum Conservation:
![(270\,kg\cdot m^{2})\cdot \left(8\,rpm\right) = [270\,kg\cdot m^{2}+(27\,kg)\cdot (1.80\,m)^{2}]\cdot \dot n](https://tex.z-dn.net/?f=%28270%5C%2Ckg%5Ccdot%20m%5E%7B2%7D%29%5Ccdot%20%5Cleft%288%5C%2Crpm%5Cright%29%20%3D%20%5B270%5C%2Ckg%5Ccdot%20m%5E%7B2%7D%2B%2827%5C%2Ckg%29%5Ccdot%20%281.80%5C%2Cm%29%5E%7B2%7D%5D%5Ccdot%20%5Cdot%20n)
Answer:
Explanation:
frequency n = 90 x 10⁶ Hz .
time period T = 1 / n
= 1 / 90 x 10⁶
= 1.11 x 10⁻⁸ S.
wavelength = velocity of light / frequency
= 3 x 10⁸ / 90 x 10⁶
= 3.33 m
maximum value of the magnetic field. ( B₀ )
E₀ / B₀ = c where E₀ and B₀ are maximum electric and magnetic field .
E₀ / c= B₀
200/ 3 x 10⁸
= 66.67 x 10⁻⁸ T .
expressions in SI units for the space and time variations of the electric field
N/C
T
Answer:
A) U₀ = ϵ₀AV²/2d
B) U₁ = (ϵ₀AV²)/6d
This means that the new energy of the capacitor is (1/3) of the initial energy before the increased separation.
C) U₂ = (kϵ₀AV²)/2d
Explanation:
A) The energy stored in a capacitor is given by (1/2) (CV²)
Energy in the capacitor initially
U₀ = CV²/2
V = voltage across the plates of the capacitor
C = capacitance of the capacitor
But the capacitance of a capacitor depends on the geometry of the capacitor is given by
C = ϵA/d
ϵ = Absolute permissivity of the dielectric material
ϵ = kϵ₀
where k = dielectric constant
ϵ₀ = permissivity of free space/air/vacuum
A = Cross sectional Area of the capacitor
d = separation between the capacitor
If air/vacuum/free space are the dielectric constants,
So, k = 1 and ϵ = ϵ₀
U₀ = CV²/2
Substituting for C
U₀ = ϵ₀AV²/2d
B) Now, for U₁, the new distance between plates, d₁ = 3d
U₁ = ϵ₀AV²/2d₁
U₁ = ϵ₀AV²/(2(3d))
U₁ = (ϵ₀AV²)/6d
This means that the new energy of the capacitor is (1/3) of the initial energy before the increased separation.
C) U₂ = CV²/2
Substituting for C
U₂ = ϵAV²/2d
The dielectric material has a dielectric constant of k
ϵ = kϵ₀
U₂ = (kϵ₀AV²)/2d
Answer:
scientists will use absolute dating to find how old a fossil exactly is.
Answer:
The correct answer is b, x = 9 cos (pi / 2 t)
Explanation:
The equation that describes a simple pendulum is
θ = θ₀ cos (wt + φ)
The angle is measured is radians
θ = x / L
We replace
d / L = x₀ / L cos (wt + φ)
x₀ = 9 in
We replace
d = 9 cos (wt + φ)
Angular velocity is related to frequency and period.
w = 2π f = 2π / T
The period is the time of a complete oscillation T = 4 s
w =2π / 4
w = π / 2
Let's replace
x = 9 cos (π/2 t + φ)
As the system is released from the root x = x₀ for t = 0 s
x₀ = x₀ cos φ
Cos φ = 1
φ = 0°
The final equation is
x = 9 cos (pi / 2 t)
The correct answer is b
