Question

If earth is supposed to be a sphere of radius R, if $g_{30}$ is value of acceleration due to gravity at latitude of 30 and g at the equator, the value of $g-g_{30}$

• A. $\frac{5}{4}{\omega }^{2}R$
• B. $\frac{3}{4}{\omega }^{2}R$
• C. ${\omega }^{2}R$
• D. $\frac{1}{4}{\omega }^{2}R$

Answer 1

The correct option is B $\frac{3}{4}{\omega }^{2}R$

correct answer is B.

Acceleration due to gravity is given by

$g^1=g-R{w}^{2}co{s}^2\lambda$

at 30,

$g_{30}=g-R{w}^{2}co{s}^2{30}^0$

$=g-\frac{3}{4}R{w}^2$

$g-g_{30}=\frac{3}{4}R{w}^2$