A coin placed on a rotating turn table just slips if it is placed at a distance of $$4 \mathrm{~cm}$$ from the centre. If the angular velocity of the turn table is doubled it will just slip at a distance of

One end of a string of length $$l$$ is connected to a particle of mass $$m$$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $$v$$, the net force on the particle (directed towards the centre) is ($$T$$ is the tension in the string)