Calculate the apparent weight of a body of mass m at a latitude `lambda` when it is moving with speed v on the surface of the earth from west to east at the same latitude.

Explanation

If W be the apparent weight of body at a latitude `lambda` then from figure shown, we have
`W = mg - m omega^(2)Rcos^(2) lambda` …(1)
When body moves at speed v from west to east relative to earth, its net angular speed `omega` can be given as
`omega = omega_(e) + (v)/(R cos lambda)` [`omega_(e) rarr` earth's angular velocity]
Now from equation (1) we have

`W = mg - m[omega_(e) + (v)/(R cos lambda)]^(2)R cos^(2) lambda`
or `W = mg - m[omega_(e)^(2)+(v^(2))/(R^(2) cos^(2) lambda) + (2 omega_(e)v)/(R cos lambda)]R cos^(2) lambda`
`= mg - m omega_(e)^(2)R cos^(2) lambda - (mv^(2))/(R ) - 2 m omega_(e) v cos lambda`
`= mg(1-(w_(e)^(2)R cos^(2) lambda)/(g) - (2 omega_(2) v cos lambda)/(g))`
[Neglecting `(mv^(2))/(R )` as being very small]