Question

The effect of rotation of the earth on the value of acceleration due to gravity is

• A. g is maximum at the equator and minimum at the poles
• B. g is minimum at the equator and maximum at the poles
• C. g is maximum at both places
• D. g is minimum at both places

Answer 1

Answer: (A)

As $g^{{}^{\prime }}=g-{\omega }^{2}R{\cos }^2\lambda$
The latitude at a point on the surface of the earth is defined as the angle, which the line joining that point to the centre of earth makes with equitorial plane. It is denoted by $\lambda$. For the poles $\lambda =90^{\circ }$ and for equator $\lambda =0^{\circ }$
(i) Substituting $\lambda =90^{\circ }$ in the above expression, we get
$g_{\text{pole }}=g-{\omega }^{2}R{\cos }^{2}90^{\circ }$
$\therefore g_{\text{pole }}=g$
ie, there is no effect of rotational motion of the earth on the value of $g$ at the poles.
(ii) Substituting $\lambda =0^{\circ }$ in the above expression, we get
$g_{\text{equator }}=g-{\omega }^{2}R{\cos }^2{0}^{\circ }$
$\therefore g_{\text{equator }}=g-{\omega }^{2}R$
ie, the effect of rotation of earth on the value of $g$ at the equator is maximum.