Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 11, Problem 68P

(a)

To determine

ToShow: The element produces a gravitational field at a point x0 on the x axis in the region x0>L is given by dg0=GML(x0x)2dx .

(a)

Expert Solution
Check Mark

Explanation of Solution

Given information :

Mass of the rod =M

Length of the rod =L

Length of an element of the rod =dx

Mass of an element of the rod =dm

Formula used :

Acceleration due to gravity for small mass element ( dm ) can be obtained by:

  dg=Gdmr2

Calculation:

The gravitational field at P due to the element dm is

  dgx=Gdmr2i^

  dm=MLdx

Distance to the point on the axis:

  r=x0x

  dgx={GML(x0x)2dx}i^

(b)

To determine

ToIntegrate: The result over the length of the rod to find the total gravitational field at the point x0 due to the rod.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given information:

Mass of the rod =M

Length of the rod =L

Length of an element of the rod =dx

Mass of an element of the rod =dm

Formula used:

The element produces a gravitational field at a point x0 on the x axis in the region x0>L is given by dg0=GML(x0x)2dx .

Calculation:

  gx=GML0Ldx(x0x)2i^gx={GML[1(x0x)]0L}i^gx=GMxo(x0L)i^

Conclusion:

The total gravitational field at the point x0 due to the rod is: gx=GMxo(x0L)i^

(c)

To determine

To Calculate: The gravitational force on a point particle of mass m0 at x0 .

(c)

Expert Solution
Check Mark

Explanation of Solution

Given information:

Mass of the rod =M

Length of the rod =L

Length of an element of the rod =dx

Mass of an element of the rod =dm

Formula used:

Force of gravity

  F=mg

Where, m is the mass and gis the acceleration due to gravity.

The total gravitational field at the point x0 due to the rod is: gx=GMxo(x0L)i^

Calculation:

By using the definition of gravitational field and the result from part (b) to express Fg at x=x0 is:

  Fg=m0gxFg=GMm0x0(x0L)i^

Conclusion:

The gravitational force on a point particle of mass m0 at x0 is Fg=GMm0x0(x0L)i^

(d)

To determine

To Show:For x0>>L , the field of the rod approximates the field of a point particle of mass M at x=0 .

(d)

Expert Solution
Check Mark

Explanation of Solution

Given information:

Mass of the rod =M

Length of the rod =L

Length of an element of the rod =dx

Mass of an element of the rod =dm

Formula used:

The total gravitational field at the point x0 due to the rod is: gx=GMxo(x0L)i^

Calculations:

  gx=GMxo(x0L)i^

  gx=GMx02(1Lx0)i^

For x0>>L , the second term in parentheses is very small.

  gxGMx02i^

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Chapter 11 Solutions

Physics for Scientists and Engineers

Ch. 11 - Prob. 11PCh. 11 - Prob. 12PCh. 11 - Prob. 13PCh. 11 - Prob. 14PCh. 11 - Prob. 15PCh. 11 - Prob. 16PCh. 11 - Prob. 17PCh. 11 - Prob. 18PCh. 11 - Prob. 19PCh. 11 - Prob. 20PCh. 11 - Prob. 21PCh. 11 - Prob. 22PCh. 11 - Prob. 23PCh. 11 - Prob. 24PCh. 11 - Prob. 25PCh. 11 - Prob. 26PCh. 11 - Prob. 27PCh. 11 - Prob. 28PCh. 11 - Prob. 29PCh. 11 - Prob. 30PCh. 11 - Prob. 31PCh. 11 - Prob. 32PCh. 11 - Prob. 33PCh. 11 - Prob. 34PCh. 11 - Prob. 35PCh. 11 - Prob. 36PCh. 11 - Prob. 37PCh. 11 - Prob. 38PCh. 11 - Prob. 39PCh. 11 - Prob. 40PCh. 11 - Prob. 41PCh. 11 - Prob. 42PCh. 11 - Prob. 43PCh. 11 - Prob. 44PCh. 11 - Prob. 45PCh. 11 - Prob. 46PCh. 11 - Prob. 47PCh. 11 - Prob. 48PCh. 11 - Prob. 49PCh. 11 - Prob. 50PCh. 11 - Prob. 51PCh. 11 - Prob. 52PCh. 11 - Prob. 53PCh. 11 - Prob. 54PCh. 11 - Prob. 55PCh. 11 - Prob. 56PCh. 11 - Prob. 57PCh. 11 - Prob. 58PCh. 11 - Prob. 59PCh. 11 - Prob. 60PCh. 11 - Prob. 61PCh. 11 - Prob. 62PCh. 11 - Prob. 63PCh. 11 - Prob. 64PCh. 11 - Prob. 65PCh. 11 - Prob. 66PCh. 11 - Prob. 67PCh. 11 - Prob. 68PCh. 11 - Prob. 69PCh. 11 - Prob. 70PCh. 11 - Prob. 71PCh. 11 - Prob. 72PCh. 11 - Prob. 73PCh. 11 - Prob. 74PCh. 11 - Prob. 75PCh. 11 - Prob. 76PCh. 11 - Prob. 77PCh. 11 - Prob. 78PCh. 11 - Prob. 79PCh. 11 - Prob. 80PCh. 11 - Prob. 81PCh. 11 - Prob. 82PCh. 11 - Prob. 83PCh. 11 - Prob. 84PCh. 11 - Prob. 85PCh. 11 - Prob. 86PCh. 11 - Prob. 87PCh. 11 - Prob. 88PCh. 11 - Prob. 89PCh. 11 - Prob. 90PCh. 11 - Prob. 91PCh. 11 - Prob. 92PCh. 11 - Prob. 93PCh. 11 - Prob. 94PCh. 11 - Prob. 95PCh. 11 - Prob. 96PCh. 11 - Prob. 97PCh. 11 - Prob. 98PCh. 11 - Prob. 99PCh. 11 - Prob. 100PCh. 11 - Prob. 101PCh. 11 - Prob. 102PCh. 11 - Prob. 103PCh. 11 - Prob. 104PCh. 11 - Prob. 105PCh. 11 - Prob. 106PCh. 11 - Prob. 107P
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