Question

The Earth is rotating with angular velocity $\omega$ about its own axis. $R$ is the radius of the Earth. If $R{\omega }^2=0.03386m/s^2$, calculate the weight of a body of mass $100$ gram at latitude ${25}^o$.
$(g=9.8m/s^2),cos{25}^{\circ }=0.9063$

Answer 1

Given $m=100g$, $w^{2}R=0.03386m/s^2$, latitude $\left(\lambda \right)={25}^o$, $g=9.8m/s^2$
$g_{\lambda }=g-w^{2}R{\cos }^2\lambda$
$=9.8-0.03386{\cos }^2{25}^o$
$=9.77219m/s^2$ $(\cos {25}^o=0.9063)$
Weight $=m{g}_{\lambda }$
$=0.1\times 9.77219$
$=0.977N$
$\therefore$ The weight of the body at latitude ${25}^o=0.977N$.