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 internal or external forces, Explain internal or external forces ...

Explain internal or external forces Forces can be internal or external. For instance the mutual attraction of atoms within a block of wood are known as internal forces. Somethi

Dimensions, find the dimensions of the following i.power ii.velocity iii.fo...

find the dimensions of the following i.power ii.velocity iii.force

Science, How comes the word physics?

How comes the word physics?

Damped oscillation, what is the physical significance of damping constent

what is the physical significance of damping constent

How much time is required to raise the temperature, how much time is requir...

how much time is required to raise the temperature of the water from A family comes home from a long vacation with laundry to-do and showers to take. The water heater has been t

Optical instrument, difference b/w concave grating and rownald mounting

difference b/w concave grating and rownald mounting

Velocity of light in moving media, Velocity of light in moving media, Sagna...

Velocity of light in moving media, Sagnac formula and its application in optical gyroscopes In 1913, the French physicist Georges Signac published some experimental results and

Sommerfield''s free electron gas model, Q.   Give the basic assumptions mad...

Q.   Give the basic assumptions made in free electron model of solid. OR Write down basic postulates of Sommerfield's free electron gas model. Show that the number of ene

Direction south to north, An alpa particle is directed vertically upward wi...

An alpa particle is directed vertically upward with a speed of 3 X 104 Km/Sec in a region where a magnetic field of magnitude 1 Tesla exists in the direction south to north. Determ

Define resistance, The characteristics of substance by virtue of which it o...

The characteristics of substance by virtue of which it opposes the flow of current by it, is called as the resistance.

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