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Physics

Mechanics

Easy

Question

The acceleration due to gravity at the poles and the equator is $g subscript p$ and $g subscript e$ respectively. If the earth is a sphere of radius $R subscript E$ and rotating about its axis with angular speed $omega$ then $g subscript p minus g subscript e$ is given by

$\frac{ω^{2}}{R_{E}}$
$\frac{ω^{2}}{R_{E}^{2}}$
$ω^{2} R_{E}^{2}$
$ω^{2} R_{E}^{}$

The correct answer is: $omega squared R subscript E superscript blank$

$g to the power of apostrophe equals g minus R subscript E omega squared cos squared lambda$
At equator, $lambda equals 0 degree comma cos 0 degree equals 1$
$therefore g to the power of apostrophe equals g subscript e equals g minus R subscript g omega squared$
At poles, $lambda equals 90 degree comma cos 90 degree equals 0$
$table attributes columnalign left end attributes row cell therefore g equals g subscript P equals g end cell row cell therefore g subscript P minus g subscript e equals g minus open parentheses g minus R subscript E omega squared close parentheses equals R subscript E omega squared end cell end table$

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