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

Two particles are projected vertically upwards with the same velocity on two different planets with accelerations due to gravity $g_1$ and $g_2$ respectively. If they fall back to their initial points of projection after lapse of times $t_1$ and $t_2$ respectively,then

The length of a seconds pendulum at a height $h=2R$ from the earth's surface will be. (Given: $R =$ radius of earth and acceleration due to gravity at the surface of earth $g = \pi^{2} \ m/s^{2}$)

At what altitude will the acceleration due to gravity be $25\%$ of that at the earth's surface (given radius of earth is $R$)?

Given below are two statements:
Statement-$I$: Acceleration due to gravity is different at different places on the surface of Earth.
Statement-$II$: Acceleration due to gravity increases as we go down below the Earth's surface.
In the light of the above statements,choose the correct answer from the options given below:

If the radius of the Earth becomes double while its mass remains unchanged,what will be the change in the weight of an object of mass $m$ on the surface of the Earth?