The value of ' g ' at certain height h above the free surface of earth is x4 where x is the value of ' g ' at the surface of earth. The height h is
Question
The value of ' g ' at certain height h above the free surface of earth is x4 where x is the value of ' g ' at the surface of earth. The height h is
Solution
The value of 'g' at a certain height 'h' above the surface of the earth is given by the formula:
g' = g * (R/(R+h))^2
where:
- g' is the value of 'g' at height 'h'
- g is the value of 'g' at the surface of the earth
- R is the radius of the earth
In this case, we know that g' = x^4 * g. We can set the two expressions for g' equal to each other and solve for h:
x^4 * g = g * (R/(R+h))^2
We can cancel out the g's and simplify:
x^4 = (R/(R+h))^2
Taking the square root of both sides gives us:
x^2 = R/(R+h)
Solving for h gives us:
h = R * ((1/x^2) - 1)
So the height 'h' is equal to the radius of the earth times the quantity one over x squared minus one.
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