A disc of circumference \( S \) stands vertically on a horizontal surface as shown in figure-5.1...

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A disc of circumference \( S \) stands vertically on a horizontal surface as shown in figure-5.145. A horizontal force \( P \) acts on the centre of the disc. Half of the circumference \( (A B C) \) is rough and the friction is sufficient to prevent slipping when the disc rolls along \( X Y \). The other half of the circumference \( (A D C) \) is smooth. The disc starts from rest when \( P \) begins to act and the point \( C \) is at the bottom. Find the distance moved by the disc along \( x y \) when it completes one rotation.
Figure \( 5.145 \)
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