A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45^o, the speed of the car is

ABC is an equilateral triangle with O as its centre. $${\overrightarrow F _1},{\overrightarrow F _2}$$ and $${\overrightarrow F _3}$$ represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then magnitude of $${\overrightarrow F _3}$$ is

The height at which the weight of a body becomes $${\left( {{1 \over {16}}} \right)^{th}}$$, its weight on the surface of earth (radius R), is

A geostationary satellite is orbiting the earth at a height of 5R above the surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of the earth is