A wheel of 1 m radius completes half rotation on horizontal path. Magnitude of displacement form the point of contact with path initially is………

Options

A. `2pi`
B. `pi`
C. `sqrt(pi^(2) + 4)`
D. `2`

Answer

C

Explanation

If wheel completes 1 rotation, that horizontal distance is `2pi r.`
Here, it completes half rotation. Hence distance covered on horizontal path `= pir = OP` and OQ =2r.
From figure `PQ ^(2) =PO^(2) + OQ^(2)`
`x^(2) = (pir) ^(2) + (2r)^(2) `
`x=1 sqrt (pi ^(2) +4) [because r =1m]`