The ratio of gravitational acceleration at height $3R$ to that at height $4R$ from the surface of the earth is (where $R$ is the radius of the earth):

The radius of the Moon is $\frac{1}{4}$ times that of the Earth,and its mass is $\frac{1}{80}$ times that of the Earth. If the acceleration due to gravity on Earth is $g$,what is the acceleration due to gravity on the Moon?

The weights of an object are measured in a coal mine of depth $h_1$,then at sea level of height $h_2=0$,and lastly at the top of a mountain of height $h_3$ as $W_1, W_2$,and $W_3$ respectively. Which one of the following relations is correct? [$h_1 \ll R, h_3 \ll R, R=$ radius of the earth]

If $R$ is the radius of the earth and $g$ is the acceleration due to gravity on the earth's surface,the mean density of the earth is

If the radius of the Earth shrinks to $1/n$ of its present value while its mass remains constant,what will be the value of $g'_e$ on its surface?

The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is $2 \ s$. The period of oscillation of the same pendulum on the planet would be