Variation in g Due to Shape of Earth
Category : JEE Main & Advanced
Earth is elliptical in shape. It is flattened at the poles and bulged out at the equator. The equatorial radius is about 21 km longer than polar radius, from \[g=\frac{GM}{{{R}^{2}}}\]
At equator \[{{g}_{e}}=\frac{GM}{R_{e}^{2}}\] ...(i)
At poles \[{{g}_{p}}=\frac{GM}{R_{p}^{2}}\] ...(ii)
From (i) and (ii) \[\frac{{{g}_{e}}}{{{g}_{p}}}=\frac{R_{p}^{2}}{R_{e}^{2}}\]
Since \[{{R}_{equator}}>{{R}_{pole}}\]
\[\therefore \] \[{{g}_{pole}}>{{g}_{equator}}\] and \[{{g}_{p}}={{g}_{e}}+0.018\,\,m{{s}^{-2}}\]
Therefore the weight of body increases as it is taken from equator to the pole.
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