A disc of radius R rolls without slipping. At t=0 the topmost material point is A. After the disc completes half a rotation, the displacement of A from its initial position is:

Question

G1 Physics · Accepted Answer

After half a rotation, the centre advances by s = Rθ = πR The original top point becomes the bottom point. Relative to its initial position, the horizontal displacement is πR and vertical displacement is 2R downward. Therefore, Δr = √[(πR)² + (2R)²] = R√(π²+4) Hence option B follows.