Given below are two statements: One is labell | vedclass

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(D) The effective acceleration due to gravity $(g')$ on the surface of the rotating Earth is given by the vector sum of the gravitational acceleration

Vedclass · Accepted Answer

$A$ is false but $R$ is true.

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(D) The effective acceleration due to gravity $(g')$ on the surface of the rotating Earth is given by the vector sum of the gravitational acceleration $(g)$ and the centrifugal acceleration $(rw^2)$.The magnitude of the effective acceleration due to gravity is $g' = \sqrt{g^2 + (rw^2)^2 - 2g(rw^2)\cos	heta}$,where $	heta$ is the latitude.As we move from the poles to the equator,the magnitude of the effective acceleration due to gravity changes because the centrifugal component varies with the latitude $	heta$.Furthermore,the direction of the effective acceleration due to gravity is not always towards the center of the Earth,except at the poles and the equator.Therefore,Assertion $A$ is false because the magnitude varies and the direction does not always point towards the center of the Earth.Reason $R$ states that at the equator,the direction of acceleration due to gravity is towards the center of the Earth. This is true because at the equator,the centrifugal acceleration $(rw^2)$ is directed radially outward,and the gravitational acceleration $(g)$ is directed radially inward. Their resultant,the effective acceleration $(g')$,is also directed radially inward towards the center of the Earth.Thus,$A$ is false but $R$ is true.

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