A coin placed on a rotating gramophone disc. remains at rest when it is at a distance of 8 cm from it's centre. The angular velocity of the disc is then doubled. At what distance from the centre the coin should be shifted,towards the centre so that it will just slip?

Explanation

C.P. force = force of friction.
`mrw^2 = mumg` `therefore r=(mug)/w^2` `therefore r alpha 1/w^2`
`r_2/r_1=(w_1/w_2)^2=1/9` `therefore r_2=9/9 = 1cm`.