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

Explain cement concrete, Explain Cement concrete Cement concrete is a m...

Explain Cement concrete Cement concrete is a mixture of cement, sand, pebbles or crushed rock and water, which where placed in the skeleton of forms and permitted to cure becom

Electrostatic shielding, Electrostatic shielding/screening is the phenomeno...

Electrostatic shielding/screening is the phenomenon of protecting a particular region of space from external electric field. Sensitive instruments and appliances are affected serio

Who female physicist who received the nobel prize in 1963, Name the female ...

Name the female physicist who received the Nobel Prize in 1963 for her discovery concerning the shell structure of the nucleus. Ans: (Maria Goeppert) Mayer was the first fe

What is permeability?, It is the property of a material by virtue of which ...

It is the property of a material by virtue of which it allows itself to be magnetized. Permeability varies from material to material depending upon the saturation and temperature.

Emf and size, is there relation between emf and size os cell?

is there relation between emf and size os cell?

Explain unit newton, NEWTON ? "The force which forms an acceleration of 1 m...

NEWTON ? "The force which forms an acceleration of 1 ms-2 in a mass of 1 kg". It is represented by N.

Explain transistor, Transistor: An active semi-conductor device with th...

Transistor: An active semi-conductor device with three terminals that is emitter base and collector is known as transistor. Types of Transistor: There are two types of

How can light be defined in simplest form, How can light be defined in simp...

How can light be defined in simplest form? The common explanation of 'light' (visible) is electromagnetic radiation visible to the human eye. It is only a little part of wha

Scalar aand vector quanties, two vectors 40N and 30N act at acute angle 3o ...

two vectors 40N and 30N act at acute angle 3o degrees to each other find the resultant vector using analytical method

MULTIPLEXERS, . Design a 32:1 multiplexer using two 16:1 multiplexers and o...

. Design a 32:1 multiplexer using two 16:1 multiplexers and one OR Gate.

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