# A mosquito is sitting on an L.P. record disc rotating on a turn table at revolutions per minute. The distance of the mosquito from the center of the turn table is lo cm. Show that the friction coefficient between the record and the mosquito is greater than it π2/81. Take g= 10 m/s2.

The rotating speed of the L.P. record is uniform as it is swiping the same amount angle in every interval. Hence, force must be central. So, the centrifugal force will try to eject the mosquito off the L.P. record.

Gravity and normal reaction will cancel each other as there is no motion of the mosquito in the vertical direction.

So,

So, to keep the mosquito stable, there must be some kind of force which is balancing the centrifugal force. This force is friction.

Centrifugal force,

The angle swiped by the mosquito in a minute will be

Now, the angular speed will be

The balance condition is

To find the required condition we need to put the value of maximum friction.

So,

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