Question

Assuming earth to be a sphere of radius $R$ , if $g^{\prime }$ is the value of acceleration due to gravity at the latitude of $30^{\circ }$ and $g$ at the equator, the value of $g-g^{\prime }$ 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
$g_{\lambda }=g-R{\omega }^{2}co{s}^2\lambda$
$\therefore g-g_{\lambda }=R{\omega }^{2}co{s}^2\lambda$
$At\lambda =30^{\circ },$
$g-g^{\prime }=R{\omega }^{2}co{s}^{2}30^{\circ }$
$=R{\omega }^2{\left(\frac{\sqrt{3}}{2}\right)}^2$
$=\frac{3}{4}R{\omega }^2$