Concept explainers
(a)
To Calculate:The value of constant
(a)
Answer to Problem 80P
Explanation of Solution
Given data:
The density of the sphere,
Radius,
Mass of the sphere,
Formula Used:
Mass = Density
Calculation:
The density of the sphere is
Here C is the constant and r is the distance.
The density of the sphere is varied by a distance so the differential element of the sphere is ,
Integrate within the limits 0 to R .
Therefore the constant C is,
Substitute
Conclusion:
The constant C is
(b)
The acceleration due to gravity for a distance
The gravitation field with in the region
(b)
Answer to Problem 80P
The acceleration due to gravity for a distance
The gravitation field with in the region
Explanation of Solution
Given data:
The density of the sphere,
Radius,
Mass of the sphere,
The constant C is
Formula used:
Gravitational field:
Here, G is the gravitational constant, M is the mass and r is the distance of the point from the center of the sphere.
Calculation:
The expression for the magnitude of gravitational field at a point outside
Substitute
Therefore, the acceleration due to gravity for a distance
The expression for the gravitational field at a point inside
Since the density of the sphere is varying with the distance, so gravitational field is given by for
Substitute
Conclusion:
The acceleration due to gravity for a distance
The gravitation field with in the region
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