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Question
Which of the following options are correct?
- Acceleration due to gravity decreases with increasing altitude.
- Acceleration due to gravity increases with increasing depth (assume the earth to be a sphere of uniform density).
- Acceleration due to gravity increases with increasing latitude.
- Acceleration due to gravity is independent of the mass of the earth.
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Solution
a, c and d
Explanation:
Acceleration due to gravity at altitude h, gh = `g/(1 + h/R)^2 ≈ g(1 - (2h)/R)`
At depth d, gd = `g(1 - d/R)`
In both cases with an increase in h and d, g decreases.
At latitude `phi`, `g_phi = g - ω^2Rcos^2 phi`
As `phi` increases `g_phi` increases
Also, we can conclude from the formulae, that it is independent of mass.
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