a) The charge on the outer surface is 
b) The number of ions is 
Explanation:
a)
The membrane behaves as a parallel plate capacitor, whose capacity is given by the equation

where
k = 4.3 is the dielectric constant
is the vacuum permittivity
is the surface area
is the distance between the two plates
Substituting,

The capacity of the membrane is related to the potential difference between the two surfaces by

where here we have
Q = excess charge on one surface
is the potential difference between the two surfaces
Solving for Q, we find

b)
We said that the net charge on the outer surface is

The charge of one K+ ions is equal to the electron charge

Therefore, the number of ions on the outer surface can be found by dividing the total charge by the charge of a single ion:

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To solve this problem it is necessary to apply the concepts related to the conservation of the Gravitational Force and the centripetal force by equilibrium,


Where,
m = Mass of spacecraft
M = Mass of Earth
r = Radius (Orbit)
G = Gravitational Universal Music
v = Velocity
Re-arrange to find the velocity



PART A ) The radius of the spacecraft's orbit is 2 times the radius of the earth, that is, considering the center of the earth, the spacecraft is 3 times at that distance. Replacing then,


From the speed it is possible to use find the formula, so



Therefore the orbital period of the spacecraft is 2 hours and 24 minutes.
PART B) To find the kinetic energy we simply apply the definition of kinetic energy on the ship, which is



Therefore the kinetic energy of the Spacecraft is 1.04 Gigajules.
Kinetic energy depends on the mass and the speed of a moving object.
If the speeds are equal, then the rick with more mass has more kinetic energy.
<h3><u>Answer</u> :</h3>
Initial velocity = zero (i.e., free fall)
Final velocity = 30m/s
Acceleration due to gravity = 10m/s²
For a body falling freely under the action of gravity, g is taken positive
◈ <u>First equation of kinenatics</u> :
⇒ v = u + gt
⇒ 30 = 0 + 10t
⇒ t = 30/10
⇒ <u>t = 3s</u>
Hence, object will attain a speed of 30m/s after 3s.
Answer: The mass of the sculpture is 11.8kg
Explanation:
Using the equation of fundamental frequency of a taut string.
f = (1/2L)*√(T/μ) .... (Eqn1)
Where
f= frequency in Hertz =80Hz
T = Tension in the string = Mg
M represent the mass of the substance (sculpture) =?
g= 9.8m/s^2
L= Length of the string=90cm=0.9m
μ= mass density = mass of string /Length of string
mass of string =5g=0.005kg
L=0.9m
μ=0.005/0.9 = 0.0056kg/m
Using (Eqn1)
80= 1/(2*0.9) √(T/0.0056)
144= √(T/0.0056)
Square both sides
20736= T/0.0056
T= 116.12N
Recall that T =Mg
116.12= M * 9.8
M=116.12/9.8
M= 11.8kg
Therefore the mass of the sculpture is 11.8kg