Acceleration due to gravity at surface of a planet is equal to that at surface of earth and density is $1.5$ times that of earth. If radius of earth is $R$, radius of planet is .................

What will be the acceleration due to gravity at height $h$ if $h >> R$. Where $R$ is radius of earth and $g$ is acceleration due to gravity on the surface of earth

The maximum vertical distance through which a fully dressed astronaut can jump on the earth is $0.5\, m$. If mean density of the moon is two-thirds that of the earth and radius is one quarter that of the earth, the maximum vertical distance through which he can jump on the moon and the ratio of time of duration of jump on the moon to that on the earth are

The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is $9 : 4$. The mass of the planet is $\frac{1}{9}^{th}$ of that of the Earth. If $'R'$ is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density)

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion $A:$ A pendulum clock when taken to Mount Everest becomes fast.

Reason $R:$ The value of $g$ (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth.

In the light of the above statements, choose the most appropriate answer from the options given below

Choose the correct statement from the following :Weightlessness of an astronaut moving in a satellite is a situation of