What is effective weight of body from this derivation?
How is g(effective) different from g(s) ?

Dear Student

Effective weight of the body is body weight when we are considering change in value fo g due to rotation and shape of earth.
Let actual weight of body of mas m is mg
Here g is actual value of g = 9.81 m/s²

$$\begin{gathered} variation of g due to rotation \\ {g}_{\lambda } =g -{\omega }^{2}R {\cos }^2\lambda \\ That is g_{\lambda } (effective g ) is less than actual value of g by {\omega }^{2}R {\cos }^2\lambda \\ At equator \lambda = 0 \\ {g}_{\lambda } =g -{\omega }^{2}R {\cos }^2\lambda \\ {g}_{\lambda } =g -{\omega }^{2}R This is minimum value of g \\ At poles \lambda = 90 \\ {g}_{\lambda } =g -{\omega }^{2}R {\cos }^2\lambda \\ {g}_{\lambda } =g \\ That is g at poles is independent of rotation of earth. It is maximum value of g \\ So similarily \\ Effective Weight of body at less than actual weight by term m{\omega }^{2}R {\cos }^2\lambda \\ m{g}_{\lambda } =mg -m{\omega }^{2}R {\cos }^2\lambda \end{gathered}$$
Regards