A hoop rolls on a horizontal ground without slipping with linear speed `v`. Speed of a particle `P` on the circumference of the hoop at angle `theta` is :

Options

A. `2 v sin (theta//2)`
B. `v sin theta`
C. `2v cos (theta//2)`
D. `v cos theta`

Answer

A

Explanation

(a) `v_p = sqrt(v^2 + v^2 + 2vv cos (180 - theta))`
`rArr v_p = sqrt(2v^2 [1- cos theta]]`
=`2 v sin (theta//2)`
.