An object is taken to a height above the surface of earth at a distance $${5 \over 4}$$ R from the centre of the earth. Where radius of earth, R = 6400 km. The percentage decrease in the weight of the object will be :

Three identical particles $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ of mass $$100 \mathrm{~kg}$$ each are placed in a straight line with $$\mathrm{AB}=\mathrm{BC}=13 \mathrm{~m}$$. The gravitational force on a fourth particle $$\mathrm{P}$$ of the same mass is $$\mathrm{F}$$, when placed at a distance $$13 \mathrm{~m}$$ from the particle $$\mathrm{B}$$ on the perpendicular bisector of the line $$\mathrm{AC}$$. The value of $$\mathrm{F}$$ will be approximately :

The radii of two planets A and B are in the ratio 2 : 3. Their densities are 3$$\rho$$ and 5$$\rho$$ respectively. The ratio of their acceleration due to gravity is :

The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be