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Question -

Adisc revolves with a speed of  rev/min, and has a radius of15 cm. Two coins are placed at 4 cm and 14 cm away from the centre of therecord. If the co-efficient of friction between the coins and the record is0.15, which of the coins will revolve with the record?



Answer -

Coinplaced at 4 cm from the centre

Mass of each coin = m

Radius of the disc, r = 15cm = 0.15 m

Frequencyof revolution, ν =  rev/min 

Coefficient of friction, μ =0.15

Inthe given situation, the coin having a force of friction greater than or equalto the centripetal force provided by the rotation of the disc will revolve withthe disc. If this is not the case, then the coin will slip from the disc.

Coin placed at 4 cm:

Radius of revolution, r‘ = 4 cm= 0.04 m

Angular frequency, ω = 2πν

 

Frictional force, f = μmg= 0.15 × m × 10 = 1.5m N

Centripetalforce on the coin:

Fcent.

= 0.49N

Since f > Fcent,the coin will revolve along with the record.

Coin placed at 14 cm:

Radius, = 14 cm = 0.14 m

Angular frequency, ω = 3.49s–1

Frictional force, f‘ = 1.5m N

Centripetalforce is given as:

Fcent.

m × 0.14 × (3.49)2

= 1.7m N

Since f < Fcent.,the coin will slip from the surface of the record.


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