A planet has a radius R and density $\rho$. If both are doubled, the acceleration due to gravity at its surface will:

At sea level, the value of $g$ is minimum at

Considering rotational motion of earth. The acceleration due to gravity at the equator of earth is given by, (where $\omega=$ angular velocity of earth, $\mathrm{R}=$ radius of earth, $\mathrm{g}=$ acceleration due to gravity)

If earth rotates $n$ time faster than its present speed $\omega$ about its axis in order that the bodies lying on the equator of earth just fly off into the space, then the value of $n$ is equal to (take radius of earth $R$ )

The weight of an object is $90 \mathrm{~kg}$ at the surface of the earth. If it is taken to a height equal to half of the radius of the earth, then its weight will beocme

A cycle wheel of radius 0.4 m completes one revolution in one second then the acceleration of a point on the cycle wheel will be

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

What is the ratio between the height ${H}$ of a mountain and the depth ${h}$ of a mine, if a pendulum swings with the same period at the top of the mountain and at the bottom of the mine? (Assume ${H} <

A particle of mass m moves with constant speed along a circular path of radius r under the action of force F. Its speed is

The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth $R$, the radius of the planet would be

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