1. Effective weight on the rotating Earth

   The weight measured on Earth is the effective weight, which is reduced by the centrifugal effect due to Earth's rotation.

   At latitude $\lambda$, the distance of the object from Earth's rotation axis is $r_\perp = R\cos\lambda$ where $R$ is the radius of Earth.

   The centrifugal acceleration is $a_c = \omega^2 r_\perp = \omega^2 R\cos\lambda$

   Its component along the radial direction reduces the effective weight. Hence effective acceleration due to gravity is $g_{\text{eff}} = g - \omega^2 R\cos^2\lambda$

   Therefore the effective weight is $W = m g_{\text{eff}} = m\left(g - \omega^2 R\cos^2\lambda\right)$

2. What happens if angular velocity $\omega$ increases?

   Since the subtracting term $\omega^2 R\cos^2\lambda$ increases with $\omega$, the effective weight decreases wherever $\cos^2\lambda \neq 0$.

3. At the poles

   At the poles, $\lambda = 90^\circ$, so $\cos 90^\circ = 0$ Therefore, $g_{\text{eff}} = g$ and there is no centrifugal reduction.

   So increasing Earth's angular velocity does not change the weight at the poles.

4. At the equator and other places

   • At the equator, $\lambda = 0^\circ$, so reduction is maximum.
   • At any place other than the poles, $\cos^2\lambda > 0$, so weight decreases.

5. Check options

   • A: Weight everywhere increases — False
   • B: Weight everywhere decreases — False (not at poles)
   • C: No change anywhere — False
   • D: Except at poles, weight decreases — True

Hence, the correct option is D.