Is the oscillation of a simple pendulum at the centre of the earth possible?

$A$ brass cube of side $a$ and density $\rho$ is floating in mercury of density $\sigma$. If the cube is displaced a bit vertically,it executes $S.H.M.$ Its time period will be

The length of a seconds pendulum is $1 \,m$ on the earth. If the mass and diameter of a planet are double that of the earth, then the length of the seconds pendulum on the planet will be: (in $\,m$)

If the length of a clock pendulum increases by $0.2 \%$ due to atmospheric temperature rise,then the loss in time of the clock per day is ........... $s$.

$A$ simple pendulum oscillates with an angular amplitude $\theta$. If the maximum tension in the string is $4$ times the minimum tension,then the value of $\theta$ is

$A$ simple pendulum is attached to the roof of a lift. If the time period of oscillation when the lift is stationary is $T$,then the frequency of oscillation when the lift falls freely will be