Question

Calculate angular velocity of the earth so that acceleration due to gravity at $60$ latitude becomes zero. (Radius of the earth $=6400km$, gravitational acceleration at poles $=10m/s^2$, $\cos 60=0.5$)

• A. $7.8\times {10}^{-2}rad/s$
• B. $0.5\times {10}^{-3}rad/s$
• C. $1\times {10}^{-3}rad/s$
• D. $2.5\times {10}^{-3}rad/s$

Answer 1

The correct option is D $2.5\times {10}^{-3}rad/s$

New acceleration due to gravity $g^{\prime }$ is given by
$g^{\prime }=g-R_e{\omega }^2{\cos }^2\lambda$
$0=10-6.4\times {10}^6{\omega }^2{\cos }^{2}60$
$\Rightarrow {\omega }^2=\frac{10}{6.4\times {10}^6{\left[0.5\right]}^2}=2.5\times {10}^{-3}rad/s$