-GMm/2r is the total energy of the mass m if it is in a circular orbit about mass M.
Given
A particle of mass m moving under the influence of a fixed mass's M, gravitational potential energy of formula -GMm/r, where r is the separation between the masses and G is the gravitational constant of the universe.
As the Gravity Potential energy of particle = -GMm/r
Total energy of particle = Kinetic energy + Potential Energy
As we know that
Kinetic energy = 1/2mv²
Also, v is equals to square root of GM/r
v = √GM/r
Put the value of v in the formula of kinetic energy
We get,
Kinetic Energy = GMm/2r
Total Energy = GMm/2r + (-GMm/r)
= GMm/2r - GMm/r
= -GMm/2r
Hence, -GMm/2r is the total energy of the mass m if it is in a circular orbit about mass M.
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Answer:
Approximately 1.62 × 10⁻⁴ V.
Explanation:
The average EMF in the coil is equal to
,
Why does this formula work?
By Faraday's Law of Induction, the EMF induced in a coil (one loop) is equal to the rate of change in the magnetic flux through the coil.
.
Finding the average EMF in the coil is similar to finding the average velocity.
.
However, by the Fundamental Theorem of Calculus, integration reverts the action of differentiation. That is:
.
Hence the equation
.
Note that information about the constant term in the original function will be lost. However, since this integral is a definite one, the constant term in won't matter.
Apply this formula to this question. Note that , the magnetic flux through the coil, can be calculated with the equation
.
For this question,
- is the strength of the magnetic field.
- is the area of the coil.
- is the number of loops in the coil.
- is the angle between the field lines and the coil.
- At , the field lines are parallel to the coil, .
- At , the field lines are perpendicular to the coil, .
Initial flux: .
Final flux: .
Average EMF, which is the same as the average rate of change in flux:
.
Answer:
An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0.
Explanation:
:)
The handle of a metal pot gets warm when the water inside the pot starts to boil