Assuming the earth to be a sphere of uniform mass density, a body weighed $$300 \mathrm{~N}$$ on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?

To project a body of mass $$m$$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $$R_E, g=$$ acceleration due to gravity on the surface of earth):

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is :

(Given $$=$$ Radius of geo-stationary orbit for earth is $$4.2 \times 10^4 \mathrm{~km}$$)

If $$\mathrm{G}$$ be the gravitational constant and $$\mathrm{u}$$ be the energy density then which of the following quantity have the dimensions as that of the $$\sqrt{\mathrm{uG}}$$ :