Answer:
C) 40,000 Joules
Explanation:
½(1000)10² - 10000 = 40000
-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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Complete Question
The complete question is shown on the first uploaded image
Compare the percent error between your value and the accepted value of 1.26 times 10-6 T · m/A. (Use the accepted value given to three significant figures in your calculation.). 100% % error = %
Answer:
The permeability of free space is 
The percentage error is % error = 5.25%
Explanation:
From the question we are told that
The slope is
, and
Generally 
So 
From the relation given in the question
![\mu_0 = \frac{2R}{N} [\frac{B}{I} ]](https://tex.z-dn.net/?f=%5Cmu_0%20%3D%20%5Cfrac%7B2R%7D%7BN%7D%20%5B%5Cfrac%7BB%7D%7BI%7D%20%5D)
Where R is the radius of the coil 
N is the number of loops of the coil = 10
Now from the question we are told that

substituting into the equation above

Substituting values


Generally the % error is mathematically represented as
%
Given that the accepted value is
Hence substituting values
%

Explanation:
It is given that,
The speed of light in vacuum is, c = 299,792,458 m/s
The permeability constant of vacuum is, 
Let
is the permittivity of free space. The relation between
is given by :




Hence, this is the required solution.
The velocity of the particle is given by the derivative of the position vector:

(a) The particle is moving in the <em>x</em>-direction when the <em>y</em>-component of velocity is zero:

But we want <em>t</em> > 0, so this never happens, unless 2<em>c</em> = <em>d</em> is given, in which case the <em>y</em>-component is always zero.
(b) Similarly, the particle moves in the <em>y</em>-direction when the <em>x</em>-component vanishes:

We drop the zero solution, and we're left with

In the case of 2<em>c</em> = d, this times reduces to <em>t</em> = <em>c</em>/(6<em>c</em>) = 1/6.