$g_e$ and $g_p$ denote the acceleration due to gravity on the surface of the Earth and another planet whose mass and radius are twice that of the Earth. Then:

If the radius of the earth shrinks by $1.5\%$ (mass remaining same),then the value of acceleration due to gravity changes by ....... $\%$.

What is the gravitational force on a particle at the centre of the Earth?

$A$ simple pendulum is oscillating with frequency $F$ on the surface of the earth. It is taken to a depth $R/3$ below the surface of the earth ($R =$ radius of earth). The frequency of oscillation at depth $R/3$ is

Given below are two statements:
Statement $I:$ Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement $II:$ Acceleration due to earth's gravity is same at a height '$h$' and depth '$d$' from earth's surface,if $h = d$.
In the light of above statements,choose the most appropriate answer from the options given below:

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