Weight of a body of mass m decreases by $1\%$ when it is raised to height $h$ above the earth’s surface. If the body is taken to a depth h in a mine, change in its weight is

The angular speed of earth, so that the object on equator may appear weightless, is $(g = 10\,m/{s^2}$, radius of earth $6400\, km$)

The acceleration due to gravity on a planet is $1.96 \,m / s ^2$. If it is safe to jump from a height of $3 \,m$ on the earth, the corresponding height on the planet will be ........ $m$

A planet of radius $R =\frac{1}{10} \times$ (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth $\frac{R}{5}$ on it and lower a wire of the same length and of linear mass density $10^{-3} \ kgm ^{-1}$ into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth $=6 \times 10^6 \ m$ and the acceleration due to gravity on Earth is $10 \ ms ^{-2}$ )

If the radius of earth shrinks by $2 \%$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately.

Which of the following statements are true about acceleration due to gravity?
$(a)\, 'g'$ decreases in moving away from the centre if $r > R$
$(b)\, 'g'$ decreases in moving away from the centre if $r < R$
$(c)\, 'g'$ is zero at the centre of earth 
$(d)\, 'g'$ decreases if earth stops rotating on its axis