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Laws Of Motion

Question
CBSEENPH11016997

A long playing record revolves with a speed of 33 1 third space rev divided by min comma and has a radius of 15 cm. Two coins are placed at 4 cm and 14 cm away from the centre of the record. If the coefficient of friction between the coins and the record is 0.15, which of the two coins will revolve with the record?

Solution
The coin will revolve along the record, if the centrifugal force on the coin is less or equal to the force of limiting friction.
If it is not so, the coin will slip.
i.e. the coin will revolve along with record only if, 
                 space space space m r omega squared less or equal than mu m g
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#6 {main}</pre>

Given here,
        Limiting space friction comma space straight mu equals 0.15
A n g u l a r space s p e e d comma space space straight omega equals 33 1 third r p m space equals space fraction numerator 10 straight pi over denominator 9 end fraction space r a d divided by straight s 

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#6 {main}</pre> 
          
            = 0.1206m
            = 12.06 cm
Therefore, the coin at a distance 4 cm will revolve along the record.