Concept explainers
(a)
ToShow: The element produces a gravitational field at a point
(a)
Explanation of Solution
Given information :
Mass of the rod
Length of the rod
Length of an element of the rod
Mass of an element of the rod
Formula used :
Acceleration due to gravity for small mass element ( dm ) can be obtained by:
Calculation:
The gravitational field at P due to the element
Distance to the point on the axis:
(b)
ToIntegrate: The result over the length of the rod to find the total gravitational field at the point
(b)
Explanation of Solution
Given information:
Mass of the rod
Length of the rod
Length of an element of the rod
Mass of an element of the rod
Formula used:
The element produces a gravitational field at a point
Calculation:
Conclusion:
The total gravitational field at the point
(c)
To Calculate: The gravitational force on a point particle of mass
(c)
Explanation of Solution
Given information:
Mass of the rod
Length of the rod
Length of an element of the rod
Mass of an element of the rod
Formula used:
Force of gravity
Where, m is the mass and gis the acceleration due to gravity.
The total gravitational field at the point
Calculation:
By using the definition of gravitational field and the result from part (b) to express
Conclusion:
The gravitational force on a point particle of mass
(d)
To Show:For
(d)
Explanation of Solution
Given information:
Mass of the rod
Length of the rod
Length of an element of the rod
Mass of an element of the rod
Formula used:
The total gravitational field at the point
Calculations:
For
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