Answers:
a) 
b) 
Explanation:
a) The centripetal acceleration 
of an object moving in a uniform circular motion is given by the following equation:
Where:
is the angular velocity of the ball
is the radius of the circular motion, which is equal to the length of the string
Then:
This is the centripetal acceleration of the ball
b) On the other hand, in this circular motion there is a force (centripetal force 
) that is directed towards the center and is equal to the tension (
) in the string:
Where 
is the mass of the ball
Hence:
This is the tension in the string
You have effectively got two capacitors in parallel. The effective capacitance is just the sum of the two.
Cequiv = ε₀A/d₁ + ε₀A/d₂ Take these over a common denominator (d₁d₂)
Cequiv = ε₀d₂A + ε₀d₁A / (d₁d₂) Cequiv = ε₀A( (d₁ + d₂) / (d₁d₂) )
B) It's tempting to just wave your arms and say that when d₁ or d₂ tends to zero C -> ∞, so the minimum will occur in the middle, where d₁ = d₂
But I suppose we ought to kick that idea around a bit.
(d₁ + d₂) is effectively a constant. It's the distance between the two outer plates. Call it D.
C = ε₀AD / d₁d₂ We can also say: d₂ = D - d₁ C = ε₀AD / d₁(D - d₁) C = ε₀AD / d₁D - d₁²
Differentiate with respect to d₁
dC/dd₁ = -ε₀AD(D - 2d₁) / (d₁D - d₁²)² {d2C/dd₁² is positive so it will give us a minimum} For max or min equate to zero.
-ε₀AD(D - 2d₁) / (d₁D - d₁²)² = 0 -ε₀AD(D - 2d₁) = 0 ε₀, A, and D are all non-zero, so (D - 2d₁) = 0 d₁ = ½D
In other words when the middle plate is halfway between the two outer plates, (quelle surprise) so that
d₁ = d₂ = ½D so
Cmin = ε₀AD / (½D)² Cmin = 4ε₀A / D Cmin = 4ε₀A / (d₁ + d₂)
Answer:
option b is correct..................
In optics, chromatic aberration (abbreviated CA; also called chromatic distortion and spherochromatism) is an effect resulting from dispersion in which there is a failure of a lens to focus all colors to the same convergence point.[1] It occurs because lenses have different refractive indices for different wavelengths of light. The refractive index of transparent materials decreases with increasing wavelength in degrees unique to each.
r₁ = distance of the point from the source = 43 km = 43000 m
I₁ = intensity of earthquake wave at distance "r₁" = 2.5 x 10⁶ W/m²
r₂ = distance of the point from the source = 1.5 km = 1500 m
I₂ = intensity of earthquake wave at distance "r₂" = ?
we know that , for a constant power , the intensity of wave is inversely proportional to the distance from the source .
I α 1/r² where I = intensity of wave , r = distance from source
hence we can write
I₁/I₂ = r₂²/r₁²
inserting the values
(2.5 x 10⁶) /I₂ = (1500/43000)²
I₂ = 2.1 x 10⁹ W/m²
