Tunnels through the earth, Physics

Assignment Help:

Q. Tunnels through the Earth

Assume a straight tunnel is cut from the surface of the earth to the opposite side through the centre.

The object is going down the tunnel and assuming that air friction is negligible we wish to determine the time it takes for the object to return to its starting point.

The only force acting on the object is gravitational. From previous problems we know that only that portion of the earth's mass contained in the sphere with radius equal to the object's height above the centre will contribute.

Let.

                                    σ =M/V

And.

                                    V =4/3π R3

Where M is the mass of the earth and V is the volume. Be the mass density of the earth. Pretentious uniform density at any radius from the center

σ =Mr/Vr.

The foremost equation for an object at any distance r from the center is

577_Tunnels through the Earth.png

The force, F is

F = mar =4/3πGσmr.

However this corresponds to the differential equation

d2r/dt2- k r = 0

Whose solution is the same as that of an object subject to a spring force without friction, which is simple harmonic motion the period is given by

2482_Tunnels through the Earth1.png

At the surface a gravitational force is the weight of the object

1459_Tunnels through the Earth2.png

Thus

g/R=4/3π σG,

so

      1045_Tunnels through the Earth3.png


Related Discussions:- Tunnels through the earth

What do you understand by sky wave propagation, What are the basic block st...

What are the basic block structure of communication system? What do you understand by sky wave propagation?

Find the operating voltage of the coolidge tube, Q. The minimum wavelength ...

Q. The minimum wavelength of X-rays produced in a Coolidge tube is 0.05 nm. Find the operating voltage of the Coolidge tube. λmin = 12400 A 0 / V = 0.5 X 10 -10 m Theref

The trigger, The Trigger In particle physics, a trigger is a system whi...

The Trigger In particle physics, a trigger is a system which uses easy criteria to rapidly decide that events within a particle detector to remain while only a small fraction o

By whcih resistivity of conductors is most affected, Resistivity of conduct...

Resistivity of conductors is most affected by (A) Composition.       (B) Temperature. (C) Pressure.             (D) Current. Ans: Resistivity of conductors is most

What was the initial velocity of the diver, The high-dive board at most poo...

The high-dive board at most pools is 3.00 m above the water. A diving instructor dives off the board and strikes the water 1.18 s later. a. What was the initial velocity of the

Application to ballistic missiles, APPLICATION TO BALLISTIC MISSILES:  ...

APPLICATION TO BALLISTIC MISSILES:  "An unpowered and unguided missile is known as ballistic missile". The path followed by ballistic missile is known as "ballistic trajectory"

AND GATE, types of ANDGATE circuit and gate operation

types of ANDGATE circuit and gate operation

Long solenoid is fabricated, A long solenoid is fabricated by closely windi...

A long solenoid is fabricated by closely winding a wire of radius 0.5 mm over a cylindrical nonmagnetic frame so that the successive turns nearly touch every other. What would be t

Explain voltmeter, Voltmeter: An electromechanical instrument which is ...

Voltmeter: An electromechanical instrument which is used to calculate potential difference among two points is known as voltmeter. Voltmeter is a modified form of a galvanom

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd