Neglecting air resistance,is the acceleration due to gravity the same for both heavy and light objects?

$A$ mine is located at depth $\frac{R}{3}$ below the earth's surface. The acceleration due to gravity at that depth in the mine is ($R = \text{radius of earth}$,$g = \text{acceleration due to gravity at surface}$).

The weight of $1 \, kg$ becomes $1/6$ on the moon. If the radius of the moon is $1.768 \times 10^6 \, m$,then the mass of the moon will be:

If a particle takes $t$ seconds less and acquires a velocity of $v \text{ m/s}$ more in falling through the same distance on two planets,where the accelerations due to gravity are $2g$ and $8g$ respectively,then:

Given below are two statements. One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A) :$ $A$ simple pendulum is taken to a planet of mass and radius,$4$ times and $2$ times,respectively,than the Earth. The time period of the pendulum remains the same on Earth and the planet.
Reason $(R) :$ The mass of the pendulum remains unchanged at Earth and the other planet. In the light of the above statements,choose the correct answer from the options given below $:$

The period of a seconds pendulum on a planet,whose mass and radius are three times that of Earth,is