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

Describe the working of ultrasonic pulse echo system, Describe the working ...

Describe the working of ultrasonic pulse echo system. The working of ultrasonic pulse echo system: The ultrasonic pulse echo system is utilized to detect flaw, estimate the

What percentage of the sample has decayed in 15 minutes, Q. The half life p...

Q. The half life period of 84Po218 is 3 minutes. What percentage of the sample has decayed in 15 minutes? 1 HLP = 3 minutes In 15 minutes, there are 3 HLPs The remaining

Doppler effect, 1. Fill a sink or bath tub with water. 2. Practice tappi...

1. Fill a sink or bath tub with water. 2. Practice tapping the cork on the surface of the water (about 3 _times per second works well) to create evenly spaced waves. 3. Tappi

Magnetic field and electric current., the magnetic field at a dictance of 2...

the magnetic field at a dictance of 2cm from the axis of a straight conductor carrying current is 12mT.Find the currentin the conductor?

Free end of reflection and refraction of waves, When a pulse is reflected f...

When a pulse is reflected from a free side, then there is no changing of medium. Crest (C) represents as crest (C) and trough (T) denotes as trough (T), Time changes by zero and

Assignment, to find coefficient of viscosity of a liquid using stok''s law

to find coefficient of viscosity of a liquid using stok''s law

Define about the modified joule-thomson, Define about the Modified Joule-Th...

Define about the Modified Joule-Thomson? Container A of variable volume V controlled by a frictionless piston immersed in a bath at temperature T.  This container is connected

What is joule cycle, What is Joule Cycle? Find the efficiency of the J...

What is Joule Cycle? Find the efficiency of the Joule cycle, consisting of two isobars and two adiabats.  Presume that the heat capacities of the gas C p and C v are constan

Demonstrate ultrasonic flaw detector in transmission mode, Demonstrate the ...

Demonstrate the typical ultrasonic flaw detector in transmission mode? A typical ultrasonic flaw detector into its transmission mode is as demonstrated below. In this w

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