Variation of g — Prelims Questions

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

At what height 'h' above the Earth's surface will the acceleration due to gravity be $1/4$th of its value at the surface? (Assume Earth's radius $R = 6400,\text{km}$)

An object weighs $W$ at the Earth's surface. What will be its weight at a depth $d = R/2$ below the Earth's surface, assuming uniform density Earth?

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

A body is taken to a height $h$ above the Earth's surface. If the decrease in the value of 'g' is $1$, then the height $h$ is (Given Earth's radius $R = 6400,\text{km}$):

At what depth 'd' below the Earth's surface will the acceleration due to gravity be $1/3$rd of its value at the surface? (Assume Earth's radius $R$)