5.37 A disc revolves with a speed of $33 \frac{1}{3}$ rev/min, 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 co-efficient of friction between the coins and the record is 0.15, which of the coins will revolve with the record ?

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Vishal Baghel | Contributor-Level 10

4 months ago

Speed of revolution of the disc, n = $33 \frac{1}{3}$ rev/min = 100/3 rpm = 100/ (3 $\times 60) = 0.56 r p s$

Angular acceleration $ω$ = 2 $π n$ = 2 $\times \frac{22}{7} \times 0.56$ = 3.492 rad/s

The coins revolve with the disc. The centripetal force is provided by the frictional force $m v^{2} / r \leq μ m g$ …. (1)

As v = r $ω$ , the above equation becomes mr $ω^{2} / r \leq μ m g$

r $\leq μ g / ω^{2}$

r $\leq$ (0.15 $\times 10) / {3.492}^{2}$ = 12 cm

For coin A, r = 4 cm

The condition (r $\leq$ 12 ) is satisfied for the coin placed at r = 4 cm, so coin A will revolve with the disc.

The condition (r $\leq$ 12 ) is not satisfied for the coin placed at r = 14 cm, so coin B will not revolve with the disc.

Speed of revolution of the disc, n = <math><mn>33</mn><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></mfrac></math> rev/min = 100/3 rpm = 100/ (3 <math><mo>×</mo><mn>60</mn><mo>)</mo><mo>=</mo><mn>0.56</mn><mi></mi><mi>r</mi><mi>p</mi><mi>s</mi></math>Angular acceleration <math><mi>ω</mi></math> = 2 <math><mi>π</mi><mi>n</mi></math> = 2 <math><mo>×</mo><mfrac><mrow><mrow><mn>22</mn></mrow></mrow><mrow><mrow><mn>7</mn></mrow></mrow></mfrac><mo>×</mo><mn>0.56</mn></math> = 3.492 rad/sThe coins revolve with the disc. The centripetal force is provided by the frictional force <math><mi>m</mi><msup><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup><mo>/</mo><mi>r</mi><mo>≤</mo><mi>μ</mi><mi>m</mi><mi>g</mi></math> …. (1)As v = r <math><mi>ω</mi></math> , the above equation becomes mr <math><msup><mrow><mrow><mi>ω</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup><mo>/</mo><mi>r</mi><mo>≤</mo><mi>μ</mi><mi>m</mi><mi>g</mi></math>r <math><mi></mi><mo>≤</mo><mi>μ</mi><mi>g</mi><mo>/</mo><msup><mrow><mrow><mi>ω</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></math>r <math><mo>≤</mo></math>  (0.15 <math><mo>×</mo><mn>10</mn><mo>)</mo><mo>/</mo><msup><mrow><mrow><mn>3.492</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></math> = 12 cmFor coin A, r = 4 cmThe condition (r <math><mo>≤</mo></math> 12 ) is satisfied for the coin placed at r = 4 cm, so coin A will revolve with the disc.The condition (r <math><mo>≤</mo></math> 12 ) is not satisfied for the coin placed at r = 14 cm, so coin B will not revolve with the disc.

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5.37 A disc revolves with a speed of $33 \frac{1}{3}$ rev/min, 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 co-efficient of friction between the coins and the record is 0.15, which of the coins will revolve with the record ?

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5.37 A disc revolves with a speed of 3313 rev/min, 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 co-efficient of friction between the coins and the record is 0.15, which of the coins will revolve with the record ?

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5.37 A disc revolves with a speed of $33 \frac{1}{3}$ rev/min, 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 co-efficient of friction between the coins and the record is 0.15, which of the coins will revolve with the record ?