Answer:
The moment of inertia of large ring is 2MR².
(A) is correct option.
Explanation:
Given that,
Mass of ring = M
Radius of ring = R
Moment of inertia of a thin ring = MR²
Moment of inertia :
Moment of inertia is the product of the mass of the ring and square of radius of the ring.
We need to calculate the moment of inertia of large ring
Using formula of moment of inertia
Where, 
= moment of inertia at center of mass
M = mass of ring
R = radius of ring
Put the value into the formula
Hence, The moment of inertia of large ring is 2MR².
Air gap means that the dielectric is air.
So <span>ε0 = </span><span>8.85 x 10^-12 [F/m].......................permitivity of free space
Lets use the equation
</span>C= ( ε0x A) / d
Where A is the area of the plate
And d the distance between the plates
d = <span>3.2-mm = 3.2 E-3 m
so ............> A = C *d /</span>ε0 = 0.20 F * 3.2 E-3 m / 8.85 x 10^-12 [F/m]
A = 7.23 E 7 [m2]
Answer: total mechanical energy of -4.6 x 10^10 j.
Explanation: the planet express is in a circular orbit around the earth and has a total mechanical energy of -4.6 x 10^10 j.
The total mechanical energy is the sum of potential energy and the kinetic energy.
For the rocket to experience the escape from earth, the total work done will be equal to maximum kinetic energy.
According to conservative of energy, maximum kinetic energy is equal to the total mechanical energy.
The work must be provided by the planet expresss rockets in order to completley escape earth will be equal to total mechanical energy of -4.6 x 10^10 j.
Step 1: Define an equation that relates the volume of a sphere to its radius.
V = 4/3*π*r3
Step 2: Take the derivative of each side with respect to time (we will define time as "t").
(d/dt)V = (d/dt)(4/3*π*r3)
dV/dt = 4πr2*dr/dt
Step 3: We are told in the problem statement that diameter is 100m, so therefore r = 50mm. We are also told the radius of the sphere is increasing at a rate of 2mm/s, so therefore dr/dt = 2mm/s. We are looking for how fast the volume of the sphere is increasing, or dV/dt.
dV/dt = 4π(50mm)2*(2mm/s)
dV/dt = 62,832 mm3/s
