Question

The acceleration due to gravity at the poles and the equator isand respectively. If the earth is a sphere of radius and rotating about its axis with angular speed , then $\mathrm { g } _ { \mathrm { p } } - \mathrm { g } _ { \mathrm { e } }$ is given by

• A.
• B. $\frac { \omega ^ { 2 } } { R _ { E } ^ { 2 } }$
• C. $\omega ^ { 2 } R _ { E } ^ { 2 }$
• D. $\omega ^ { 2 } R _ { E }$

Answer 1

Answer: (D)

$\omega ^ { 2 } R _ { E }$

Answer 2

Accelerations due to gravity at a place of latitude $\lambda$due to the rotation of earth is

$g ^ { \prime } = g - R _ { E } \omega ^ { 2 } \cos ^ { 2 } \lambda$

At equator, $\lambda = 0 ^ { \circ } , \cos 0 ^ { \circ } = 1$

$\therefore \quad \mathrm { g } ^ { \prime } = \mathrm { g } _ { \mathrm { e } } = \mathrm { g } - \mathrm { R } _ { \mathrm { E } } \omega ^ { 2 }$

At poles, $\lambda = 90 ^ { \circ } , \cos 90 ^ { \circ } = 0$

$\therefore$

$\therefore$