Earth is assumed to be a sphere of radius R . If ' g _ ' is value of effective acceleration due to gravity at latitude 30^ and ' g ' is the value at equator, then the value of |g-g_ | is ( is angular velocity of rotation of earth, 30^ = 3 2 )

Step-by-step solution

The formula for acceleration due to gravity at certain latitude is given as g _ = g _ surface - R ^2 ^2 At equator, =0^ g = g _ surface - R ^2 0^ = g _ surface - R ^2... (i) At =30^ g _ = R ^2 30^ = g _ surface - 3 R ^2 4 ... (ii) aligned & | g - g _ |= ( g _ surfince -R ^2 )- ( g _ surface - 3 R ^2 4 )... [ From (i) and (ii)] & | g - g _ ⁻ |=R ^2 (1- 3 4 ) & | g _ - g |= R ^2 4 aligned