$A$ point mass of $10 \,kg$ is placed at the centre of the Earth. The weight of the point mass is

$A$ tunnel is dug through the centre of the earth. Show that a body of mass $m$ when dropped from rest from one end of the tunnel will execute simple harmonic motion.

The dependence of acceleration due to gravity $g$ on the distance $r$ from the centre of the earth,assumed to be a sphere of radius $R$ of uniform density,is as shown in the figure below. The correct figure is:

Match Column-$I$ with Column-$II$.

Column-$I$	Column-$II$
$(1)$ Maximum value of acceleration due to gravity $g$	$(a)$ At the center of the Earth
$(2)$ Minimum value of acceleration due to gravity $g$	$(b)$ At the poles
$(3)$ Zero value of acceleration due to gravity $g$	$(c)$ At the equator

Starting from the centre of the earth having radius $R$,the variation of $g$ (acceleration due to gravity) is shown by:

At what height above the Earth's surface does the acceleration due to gravity become $1\%$ of its value at the Earth's surface (in $R$)? (Radius of Earth $= R$)