Question

Assuming earth to be a sphere of radius $R$ , if $g'$ is the value of acceleration due to gravity at the latitude of $30^\circ $ and $g$ at the equator, the value of $g-g' \, $ is

• A. $\frac{1}{4}\omega ^{2}R$
• B. $\frac{3}{4}\omega ^{2}R$
• C. $\omega ^{2}R$
• D. $\frac{1}{2}\omega ^{2}R$

Answer 1

Answer: (B)

The value of acceleration due to gravity at latitude $\lambda$ is given by
$ \, \, \, g_{\lambda }=g-R\omega ^{2}c o s^{2}\lambda $
$\therefore \, \, \, g-g_{\lambda }=R\omega ^{2}c o s^{2}\lambda $
$ \, \, At \, \lambda =30^\circ ,$
$ \, g-g'= \, R\omega ^{2}cos^{2}30^\circ $
$=R \omega^2\left(\frac{\sqrt{3}}{2}\right)^2$
$ \, \, =\frac{3}{4}R\omega ^{2}$