Concept explainers
If you stood atop a ladder that was so tall that you doubled your distance from Earth’s center, how would your weight compare with its present value?
To compare:Actual weight with the present value.
Answer to Problem 58A
Weight of the body is decreased by its one-fourth as compared with weight of the body on the surface of the earth
Explanation of Solution
Given:
A body stood at a height equal to the radius of the Earth.
Formula used:
Weight of a body is nothing but the product of mass of the body and acceleration due to gravity ( g ).
Weight of an object is equal to the gravitational force acting on the object of mass m
(1)
Where,
Gis the Gravitational constant=
M is Earth’s mass
m is object’s mass
R is Earth’s radius
Calculation:
From equation (1), acceleration due to gravity on the surface of the earth is,
Acceleration due to gravity at height h from the surface of the earth is,
Where,
In this case, the height above the surface of the earth is equal to R so
The ratio will be
This shows that acceleration due to gravity above the surface of the Earth is 1/4 th to the acceleration due to gravity on the surface of the earth (distance R).
Multiply above equation by mass of the body so as to get the weight of the body.
Conclusion:
Therefore, weight of the object is one fourth of the value when compared with the weight of the object on the surface of the earth.
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Conceptual Physics: The High School Physics Program
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