A simple pendulum doing small oscillations at a place $\mathrm{R}$ height above earth surface has time period of $T_1=4 \mathrm{~s}$. $T_2$ would be it's time period if it is brought to a point which is at a height $2 R$ from earth surface. Choose the correct relation $[R=$ radius of Earth]:

The height at which the weight of the body become $\frac{1}{9}^{th}$. Its weight on the surface of earth (radius of earth $R$)

Imagine a new planet having the same density as that of earth but it is $3$ times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is $g$ and that on the surface of the new planet is $g^{\prime}$, then

If acceleration due to gravity at distance $d[ < R]$ from the centre of earth is $\beta$, then its value at distance $d$ above the surface of earth will be [where $R$ is radius of earth]

If all objects on the equator of earth feel weightless then the duration of the day will nearly become ....... $hr$

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.