A wheel of radius 1m rolls forward half a revolution on

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A wheel of radius 1m rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is

1. π
2. 2π
3. √2π
4. √π² + 4

Correct Option: D

Linear distance moved by wheel in half revolution = πr. Point P₁ after half revolution reaches at P₂ vertically 2m above the ground.
∴ Displacement P₁P₁
= √π²r² + 2² = √π² + 4
[ ∵ r = 1m]