Question

The difference in the value of ${}^{\prime }{g}^{\prime }$ at pole and at a latitude is $\frac{3}{4}R{w}^2$ then latitude angle is:

• A. ${60}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${95}^{\circ }$

Answer 1

The correct option is A ${60}^{\circ }$

The effective value of $g$ at any latitude angle $\theta$ is :

$\Rightarrow g_{eff}=g-{\omega }^{2}R{\cos }^2\theta$ (where $\omega =$ angular velocity of earth and $R=$ radius)

$\Rightarrow g-{\omega }^{2}R{\cos }^2\theta =\frac{3}{4}R{\omega }^2$

$\Rightarrow {\cos }^2\theta =\frac{g}{R{\omega }^2}-\frac{3}{4}$

On substituting $g=9.8m/s^2,R=6400km$ and $\omega =\frac{2\pi }{T}$ Where $T=204$ hours

${\cos }^2\theta =\frac{1}{4}$

$\Rightarrow \cos \theta =\frac{1}{2}$

So, $\theta ={60}^{\circ }$ is the latitude