Acceleration due to Gravity — Prelims Questions

An object is taken to a height $h$ above the Earth's surface. If the radius of the Earth is $R_E$, and the acceleration due to gravity at the surface is $g$, what is the approximate acceleration due to gravity at height $h$ for $h ll R_E$?

If the Earth suddenly stops rotating, what will be the effect on the value of acceleration due to gravity ($g$) at the equator?

An object weighs $W$ at the Earth's surface. What will be its weight at a depth of $R_E/4$ below the Earth's surface, where $R_E$ is the radius of the Earth?

At what height above the Earth's surface will the acceleration due to gravity be $1/4$th of its value at the surface? (Given $R_E$ is the radius of the Earth)

A body is projected vertically upwards from the Earth's surface. If air resistance is negligible, what is the acceleration of the body at its maximum height?

If the radius of the Earth shrinks by 1% (mass remaining constant), what will be the percentage change in the acceleration due to gravity ($g$) at its surface?

Which of the following statements about acceleration due to gravity ($g$) is INCORRECT?