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7.Gravitation
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If earth is supposed to be a sphere of radius R, if $g_{30}$ is value of acceleration due to gravity at latitude of $ 30^\circ$ and g at the equator, the value of $g - {g_{{{30}^o}}}$ is
A
$\frac{1}{4}{\omega ^2}R$
B
$\frac{3}{4}{\omega ^2}R$
C
${\omega ^2}R$
D
$\frac{1}{2}{\omega ^2}R$
Solution
(b) Acceleration due to gravity at latitude $\lambda$ is given by
$g' = g – R{\omega ^2}{\cos ^2}\lambda $
At ${30^o},\,\,{g_{30^\circ }} = g – R{\omega ^2}{\cos ^2}{30^o} = g – \frac{3}{4}R{\omega ^2}$
$g – {g_{30}} = \frac{3}{4}{\omega ^2}R.$
Standard 11
Physics
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