Question 705019

SCQMEDIUM

A record player stylus moves along a spiral groove cut on an annular portion of a disc with inner radius 4 cm4 \text{ cm} and outer radius 10 cm10 \text{ cm}. If the record turns 100100 times when playing, the stylus travels approximately

(A)

2.2 m

(B)

4.4 m

(C)

22 m

(D)

44 m

Detailed Solution

The average radius is ravg=(4+10)/2=7 cm=0.07 mr_{avg} = (4 + 10) / 2 = 7 \text{ cm} = 0.07 \text{ m}. The circumference is 2πravg=2×3.14×0.07=0.4396 m2 \pi r_{avg} = 2 \times 3.14 \times 0.07 = 0.4396 \text{ m}. For 100100 turns, distance =100×0.4396=43.96 m≈44 m= 100 \times 0.4396 = 43.96 \text{ m} \approx 44 \text{ m}.

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