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

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

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will