Question

The value of acceleration due to gravity on the earth at a place having a latitude of ${30}^0$. $(g=9.8m/s^2)$ is

• A. $9.77$ $m{s}^{-2}$
• B. $8.77$ $m{s}^{-2}$
• C. $7.76$ $m{s}^{-2}$
• D. $5.77$ $m{s}^{-2}$

Answer 1

The correct option is A $9.77$ $m{s}^{-2}$

The angular speed($\omega$) of Earth is approximately $7.3\times {10}^{-5}{s}^{-1}$.
$\omega =7.3\times {10}^{-5}{s}^{-1}$.
The variation in acceleration due to gravity with latitude is given by:
$g^{{}^{\prime }}=g(1-R{\omega }^{2}Co{s}^2\lambda )$
$g^{{}^{\prime }}=9.8(1-6400\times {10}^3\times (7.3\times {10}^{-5}{)}^2\times co{s}^2{30}^{\circ })$
$g^{{}^{\prime }}=9.8(1-0.034\times (\sqrt{3}/2{)}^2)=9.77m/s$