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A circular path is made from two concentric circular rings in such a way that the smaller ring when allowed to roll over the circumference of the bigger ring, it takes three full revolutions. If the area of the path way is n times the area of the smaller ring, then n is equal to
  • a)
    4
  • b)
    6
  • c)
    8
  • d)
    10
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A circular path is made from two concentric circular rings in such a w...
Let the radius of the smaller and bigger rings be r and R respectively
Circumference of the bigger ring = 3 × Circumference of the smaller ring [∵ Distance traversed in 1 revolution = Circumference of the ring]
⇒ 2πR = 3 × 2πr
⇒ R = 3r
Area of the path = Area of bigger circle – Area of small circle
⇒ πR2 – πr2
⇒ π(3r)2 – πr2 = 8 πr2 = 8 × Area of smaller ring
∴ n = 8
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A circular path is made from two concentric circular rings in such a way that the smaller ring when allowed to roll over the circumference of the bigger ring, it takes three full revolutions. If the area of the path way is n times the area of the smaller ring, then n is equal toa)4b)6c)8d)10Correct answer is option 'C'. Can you explain this answer?
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