2016 · Q28
A circular coin of radius 1 cm is allowed to roll freely on the periphery over a circular disc of radius 10 cm. If the disc has no movement and the coin completes one revolution rolling on the periphery over the disc and without slipping, then what is the number of times the coin rotated about its centre?
general-mental-abilityquantitative-aptitude
- A10
- B10.5
- C11
- D12
Explanation
When a coin of radius r rolls without slipping around a fixed disc of radius R, the coin rotates (R + r)/r times, not R/r times, because the coin's centre itself revolves once around the disc. Here (10 + 1)/1 = 11 rotations. The naive ratio of circumferences (10) misses the extra rotation due to the revolution of the centre. Note: one published key gives (A) 10, which is the common error this question is designed to expose.