A mosquito rests on an L.P. record disc that is rotating on a turn table at 33 1 3 revolutions per minute. If the distance of the mosquito from the centre of the turn table is 10 cm , what is the minimum friction coefficient required between the record and the mosquito to prevent it from slipping? Take g = 10 m/s ^2 .

Step-by-step solution

The angular velocity of the turn table is given by = 33 1 3 rev/min . Converting to radians per second: = 100 3 2 60 = 10 9 rad/s The distance of the mosquito from the centre is r = 10 cm = 0.1 m . For the mosquito to not slip, the static friction must provide the necessary centripetal force: m g m ^2 r ^2 r g Substituting the values: ( 10 9 )^2 0.1 10 100 ^2 81 1 100 ^2 81 The minimum friction coefficient required is ^2 81 .