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 θ is

Question

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 θ is <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/b0e49a076b9a3fcf9061b0f07b6e2799-.png" /> (A) 2v sin (θ/2) (B) v sin θ (C) 2v cos (θ/2) (D) v cos θ

Tardigrade Admin · Accepted Answer

vp=√v2+v2+2vv cos(180-θ) ⇒ vp=√2v2[1-cos θ] =2v sin (θ/ 2) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/4733c5ef103fca7cf5fbd1d8d0cec2bb-.png" />

Q. 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 $θ$ is

$2 v s in (θ /2)$

$v s in θ$

$2 v cos (θ /2)$

$v cos θ$

$v_{p} = v^{2} + v^{2} + 2 vv cos (180 - θ)$
$\Rightarrow v_{p} = 2 v^{2} [1 - cos θ]$
$= 2 v s in (θ /2)$

Q. 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 θ is

2vsin(θ/2)

vsinθ

2vcos(θ/2)

vcosθ