Answer:
Q1_new = 515.68 µC
Q2_new = 246.82 µC
Explanation:
Since the capacitors are charged in parallel and not in series, then both are at 250 V when they are disconnected from the battery.
Then it is only necessary to calculate the charge on each capacitor:
Q1 = 5.85 µF * 250 V = 1462.5 µC
Q2 = 2.8 µF * 250 V = 700 µC
Now, we will look at 1462.5 µC as excess negative charges on one plate, and 1462.5 µC as excess positive charges on the other plate. Now, we will use this same logic for the smaller capacitor.
When there is a connection of positive plate of C1 to the negative plate of C2, and also a connection of the negative plate of C1 to the positive plate of C2, some of these excess opposite charges will combine and cancel each other. The result is that of a net charge:
1462.5 µC - 700 µC = 762.5 µC
Thus,762.5 µC of net charge will remain in the 'new' positive and negative plates of the resulting capacitor system.
This 762.5 µC will be divided proportionately between the two capacitors.
Q1_new = 762.5 µC * (5.85/(5.85 + 2.8)) = 515.68 µC
Q2_new = 762.5 µC * (2.8/(5.85 + 2.8) = 246.82 µC
The work needed to pump the water would have the units of Joules or Pa*m^3. From here, this would be a hint that you only multiply the hyraulic pressure and its volume.
Hydraulic pressure = density*gravity*height = 1000*9.8*3.1 = 30,411 Pa
Volume = 21*14*3.1 = 911.4 m^3
Work = 30,411*911.4 = 27,716,585.4 J = 27.72 MJ
If you're careful, you ought to be able to observe ANY of these properties
without any effect on the substance:
Absorption, albedo, angular momentum, area, color, concentration,
density, elasticity, electric charge, electrical conductivity, flow rate,
electrical impedance, electric potential, fluidity, length, location, mass,
luminance, luminescence, luster, magnetic field, momentum, opacity,
permeability, permittivity, plasticity, pressure, radiance, solubility, spin,
specific heat, resistivity, reflectivity, refractive index, temperature,
thermal conductivity, velocity, viscosity, or volume.
Explanation:
It is known that relation between velocity and height is as follows.
v = 
where, g = acceleration due to gravity = 9.8 
h = height = 0.2 m
Therefore, velocity is calculated as follows.
v =
= 
= 3.92 m/s
Also,
Putting the given values into the above formula as follows.
= 
= 
= 
m/s
or, = 
m/s
Thus, we can conclude that recoil speed of the Earth is m/s.
Momentum of an object is calculated by multiplying the mass by the velocity.
p = mv
where:
p = momentum
m = mass
v = velocity
Let's take your given into account and put it in the equation:
p = mv
30,000 kg.m/s = (400kg)v
Velocity is our unknown, so to get it all we need to do is transfer mass (m) to the other side of the equation and isolate the velocity (v). When we do this, we need to use the opposite operation (rules of transposition).
(30,000kg.m/s)/(400kg) = v
Cancel out the kg and you are left with m/s.
75m/s = v
The answer is then D. 75 m/s.
Now for your second question, as you can see in the formula, mass and velocity is directly proportional to momentum. That means that the higher the mass or the velocity, the higher the momentum.
So if the velocity increases, the momentum increases as well.
