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

Heat therapy - microwave diathermy, Microwave diathermy The microwave ...

Microwave diathermy The microwave diathermy can be produced in special tube which can be placed several inches from the region to be treated . Microwave can penetrate deep int

Explain ultraviolet radiation, A metal has a work function of 4.80 eV. ...

A metal has a work function of 4.80 eV. Will ultraviolet radiation with a wave length of 385 nm be able to eject a photoelectron from the metal?

How much should be the voltage of an x-ray tube, Q. How much should be the ...

Q. How much should be the voltage of an X-ray tube so that the electrons emitted from the cathode may give an X-ray of wavelength 1 A o after striking the target?  λmin = 124

Angular velocity is contiguously decreasing, Which graph represents the ang...

Which graph represents the angular velocity as function of time in which the magnitude of angular velocity is contiguously decreasing? Ans) That is down parabola from origin gra

How much temperature copper constantan is used for measuring, Copper consta...

Copper constantan is used for measuring temperature up to (A) 1400 o C (B) 800 o C. (C) 1100 o C. (D) 400 o C.  Ans: Copper constantan is used for meas

Magnetism, how to find neutral point in a system of magnets

how to find neutral point in a system of magnets

Number of neutron, Number of neutron in C 12   is (1)6 (2)7      ...

Number of neutron in C 12   is (1)6 (2)7      (3)8 (4)9 Ans: (1)6

Absorbance spectrophotometer , Absorbance spectrophotometer: A schemat...

Absorbance spectrophotometer: A schematic diagram of a simple instrument that is used to measure the absorption of visible light is shown in Figure below. When studyin

Measure the current through resistor, For this circuit which of the subsequ...

For this circuit which of the subsequent represents a correct way of connecting an ammeter to measure the current through resistor R2? Answer: An ammeter acts simila

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