If earth stands still what will be its effect on man's weight

The correct option is Increases.

To understand why a person's weight would increase if the Earth stopped rotating, we need to look at the factors that determine our apparent weight on Earth.

The apparent acceleration due to gravity ($g^{\prime }$) at any latitude $\lambda$ on the rotating Earth is given by the formula:

$g^{\prime }=g-R{\omega }^2{cos}^2\lambda$

where:
- $g$ is the acceleration due to gravity on a non-rotating Earth.
- $R$ is the radius of the Earth.
- $\omega$ is the angular velocity of the Earth's rotation.
- $\lambda$ is the latitude of the person's location.

The term $R{\omega }^2{cos}^2\lambda$ represents the outward centrifugal acceleration due to the Earth's rotation, which counteracts gravity and slightly reduces a person's apparent weight.

If the Earth stands still, its rotation stops completely, meaning the angular velocity becomes zero:

$\omega =0$

Substituting $\omega =0$ back into our equation gives:

$g^{\prime }=g-R(0{)}^2{cos}^2\lambda$

$g^{\prime }=g$

Since the subtracting term becomes zero, the effective acceleration due to gravity ($g^{\prime }$) increases to its maximum value ($g$) everywhere on Earth (except at the poles, where $\lambda =90°$ and the rotation had no effect anyway).

Since weight is defined as $W=m{g}^{\prime }$ (where $m$ is mass), an increase in the effective acceleration due to gravity directly results in an increase in the weight of a person.