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. `(mv^(2))/(R )`
B. `(1)/(2)(mv^(2))/(R )`
C. `(mv_(e )^(2))/(R )`
D. `(mv_(e )^(2))/(R )`

Explanation

To solve the problem, we need to analyze the weight of a body in two different scenarios: when the body is at rest in a train and when the train is moving with a certain velocity around the equator.

### Step-by-Step Solution:

1. **Understanding Weight at Rest**:
The weight of a body at rest in the train is given by:
\[
W_r = m \cdot g
...