A newly discovered planet has a density eight times the density of the earth and a radius twice the radius of the earth. The time taken by $2\, kg$ mass to fall freely through a distance $S$ near the surface of the earth is $1$ second. Then the time taken for a $4\, kg$ mass to fall freely through the same distance $S$ near the surface of the new planet is ……. $\sec$.

$T$ is the time period of simple pendulum on the earth's surface. Its time period becomes $x T$ when taken to a height $R$ (equal to earth's radius) above the earth's surface. Then, the value of $x$ will be:

A clock $S$ is based on oscillation of a spring and a clock $ P$ is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having the same density as earth but twice the radius

If mass of earth decreases by $25 \%$ and its radius increases by $50 \%$, then acceleration due to gravity at its surface decreases by nearly ……… $\%$

Mass of moon is $7.34 \times {10^{22}}\,kg$. If the acceleration due to gravity on the moon is $1.4\,m/{s^2}$, the radius of the moon is $(G = 6.667 \times {10^{ – 11}}\,N{m^2}/k{g^2})$