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# Equivalence Principle

The equivalence principle deals with the equivalence of gravitational and inertial mass. The equivalence principle states that gravity is not able to recognized from uniform acceleration.

Newtonâ€™s equation of motion in a gravitational field is:

(inertial mass)*(acceleration)=(intensity of the gravitatioal field)*(gravitational mass)

If an observer discovers the presence of a force that acts on every objects in direct proportion to the inertial mass of each object, the observer is in a frame of reference which is accelerated.

There are three forms of the equivalence principle: weak (Galilean), Einsteinian, and strong. The weak equivalence principle is known as the universality of free fall or the Galilean equivalence principle. The strong EP covers the bodies with gravitational binding energy. The weak EP assumes falling bodies are bound by a non-gravitational force.

The force on M1 due to the gravitational field of M0 is:

F_1= (M_0^act M_1^pass)/r^2

Conversely, the force on a second object of arbitrary mass2 due to the gravitational field of mass0 is:

F_2= (M_0^act M_2^pass)/r^2

### Equivalence value of the Christoffel tensor of the second kind.

Prove that Christofel^a_ab = (del/delx^b)log g^(1/2) The complete problem is in the attached file.

### Prove that the divergence of a tensor T^(ab) is given

Prove that the divergence of a tensor T^(ab) is given by T^(ab) , a = [1/g^(1/2)] [del {g^(1/2) T^(ab)/delx] + [ (christoffel symbol)^b_( alpha a ) T^( alpha a ) The complete problem is in the attached file.

### A set of quantities , whose inner product with an arbitrary vector is a tensor, then prove that the set of quantities is itself a tensor.

A set of quantities , whose inner product with an arbitrary vector (that is, a contravariant tensor of rank one) is a tensor, then prove that the set of quantities is itself a tensor.

### Prove that the Christoffel's symbols are not tensors.

Prove that the Christoffel's symbols are not tensors.

### Determine Electric Field & Calculate Speed of Electrons

Please see attached file. For 1st problem, I used the formula: E1= Kq1/r2 = (8.99 x 10^9 NM/C^2)(-6.75 x 10^-6 C)/ (2.45 x 10^2 m)^2 E1= -10.109 x 10^7 N/C which = -1.01 x 10^8? Is this right? I had to convert r to p(d)from 24.5cm into m (scientific notation) - Not sure if I converted it correctly? 24.5 cm = 2.45 x 10^2 m?

### Postulates of the Special Theory of Relativity

1. State and explain the postulates of the special theory of relativity. 2. Suppose a person riding on top of a freight car shines a searchlight beam in the direction in which the train is traveling. Compare the speed of the light beam relative to the ground when: a.The train is at rest. b. The train is moving. How do

### Time Elapsed on a Clock

See attached file for full problem description. A good approximation to the metric outside the surface of the Earth is provided. It may be thought of as the familiar Newtonian gravitational potential. Here G is newton's constant and M is the mass of the earth. For this problem o may be assumed to be small. Imagine a clo

### Rotating Charge of an Insulating Rod

A charge of 4.0 x 10^-6 C is placed on a small conducting sphere that is located at the end of a thin insulating rod whose length is 0.20 m. The rod rotates with an angular speed of 150 radians/second about an axis that passes perpendicularly through its other end. What is the magnetic moment of the rotating charge?

### Buoyant force as applied to an iron block submerged in water

A block of iron is suspended from one end of an equal-arm balance by a thin wire. To balance the scales, 2.35 kg are needed on the scale pan at the other end. A) What is the volume of the block? B) Next, a beaker of water is placed so that the iron block, suspended as in part (A), is submerged in the beaker but not touch

### Vibrational frequency, Earth mass, harmonic function, hydrogen atom degeneracy

See attached file for full problem description and clarity in symbols. 1. a) In the infrared spectrum of H79Br, there is an intense line at 2630 cmÂ¡1. Calculated the force constant of H79Br and the period of vibration of H79Br. b) The force constant of 79Br79Br is 240 N Â¢mÂ¡1. Calculated the fundamental vibrational freque