The mass and diameter of a planet have twice the value of the corresponding parameters of Earth. Acceleration due to gravity on the surface of the planet is ........ $m/s^2$.

Consider a particle of mass $m$ suspended by a string at the equator. Let $R$ and $M$ denote the radius and mass of the Earth. If $\omega$ is the angular velocity of rotation of the Earth about its own axis,then the tension on the string will be $(\cos 0^{\circ}=1)$

The depth at which acceleration due to gravity becomes $\frac{g}{2n}$ is ($R=$ radius of earth,$g=$ acceleration due to gravity on earth's surface,$n$ is an integer).

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?

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude,which of the following is not correct?

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: