Consider a point P as the contact point of a wheel on ground which rolls on ground without slipping. Value of displacement of point P when wheel completes half of rotation (Ifradius of wheel is 1 m)

Options

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

Answer

B

Explanation

In half rotation point P has moved horizontally.
`(pid)/2=pir=pixx1m=pim` `[because` radius=1m`]`
In the same time, it has moved vertically a distance which is equal to its diameter = 2 m.
`therefore` Displacement of P = `sqrt(pi^(2)+2^(2))=sqrt(pi^(2)+4)`m