Weight of a body depends directly upon acceleration due to gravity `g`. Value of `g` depends upon many factors. It depends upon the shape of earth, rotation earth etc. Weight of a body at a pole is more then that at a place on equator because g is maximum at poles and minimum on equator. Acceleration due to gravity g varies with latitude `lambda` as per relation given below :
`g_(rot)=g-Romega^(2)cos^(2)lambda` where `R` is radius of earth and `omega ` is angular velocity of earth. A body of mass `m` weighs `W_(r )` in a train at rest. The train then begins to run with a velocity v around the equator from west to east. It observed that weight `W_(m)` of the same body in the moving train is different from `W_(r )`. Let `v_(e )`be the velocity of a point on equator with respect to axis of rotation of earth and R be the radius of the earth. Clearly the relative between earth and trainwill affect the weight of the body.
Difference between Weight `W_(r )` and the gravitational attraction on the body can be given as

Options

A. `g_(p)-1/4Romega^(2)`
B. `g_(p)+1/4Romega^(2)`
C. `g_(p)-1/2Romega^(2)`
D. `g_(p)+1/2Romega^(2)`

Answer

A