A particle moves through angular displacement θ on a circular path of radius r. The linear displacement will be :

Question

A particle moves through angular displacement θ on a circular path of radius r. The linear displacement will be : (A)  2r sin(θ /2)  (B)  2r cos(θ /2)  (C)  2r tan(θ /2)  (D)  2r cot(θ /2)

Tardigrade Admin · Accepted Answer

Δ vec r = vec r 2- vec r 1, where r2=r1=r <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/75e717d44aacb529bfc7d987cb87de9d-.png" /> Hence, Δ r=√r22+r12-2 r2 r1 cos θ =2 r sin (θ/2)

Q. A particle moves through angular displacement $θ$ on a circular path of radius $r$ . The linear displacement will be :

$2 r sin (θ /2)$

$2 r cos (θ /2)$

$2 r t an (θ /2)$

$2 r cot (θ /2)$

$Δ r = r_{2} - r_{1}$ ,
where $r_{2} = r_{1} = r$

Hence, $Δ r = r_{2}^{2} + r_{1}^{2} - 2 r_{2} r_{1} cos θ$
$= 2 r sin \frac{θ}{2}$

Q. A particle moves through angular displacement θ on a circular path of radius r. The linear displacement will be :

2rsin(θ/2)

2rcos(θ/2)

2r tan(θ/2)

2rcot(θ/2)