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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?

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? Correct Answer 10

Given:

Radius of circular disc = 10cm

Radius of coin = 1cm

Concept:

To do a single revolution a coin is covering its length equal to its circumference

Formula used:

Circumference of a circle = 2π× (radius)  

Calculation:

Circumference of a disc = 2 π × (10) = 20π = total distance covered by a coin

Circumference of coin = 2 π × (1) = 2π = distance covered in a single revolution

Number of turns a coin have to take for rolling on the periphery over the disc and without slipping

⇒ (20π /2π ) = 10

∴ the required number of turns = 10

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