Consider a planet whose density is same as that of the earth but whose radius is three times the radius '$$R$$' of the earth. The acceleration due to gravity '$$\mathrm{g}_{\mathrm{n}}$$' on the surface of planet is $$\mathrm{g}_{\mathrm{n}}=\mathrm{x}$$. $$\mathrm{g}$$ where $$\mathrm{g}$$ is acceleration due to gravity on surface of earth. The value of '$$\mathrm{x}$$' is

A thin rod of length '$$L$$' is bent in the form of a circle. Its mass is '$$M$$'. What force will act on mass '$$m$$' placed at the centre of this circle?

( $$\mathrm{G}=$$ constant of gravitation)

A body weighs $$300 \mathrm{~N}$$ on the surface of the earth. How much will it weigh at a distance $$\frac{R}{2}$$ below the surface of earth? ( $$R \rightarrow$$ Radius of earth)

A seconds pendulum is placed in a space laboratory orbiting round the earth at a height '$$3 \mathrm{R}$$' from the earth's surface. The time period of the pendulum will be ( $$R=$$ radius of earth)