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

The linear displacement, vec triangle r = r 2- r 1 ; where r 2= r 1= r Hence, |Δ r |=√ r 22+ r 12-2 r 2 r 1 cos θ Longrightarrow|Δ r |=√2 r 2-2 r 2 cos θ Longrightarrow|Δ r |=√2 r √1- cos θ Longrightarrow|Δ r |=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

$2 r sin (\frac{θ}{2})$

$2 r cos (\frac{θ}{2})$

$2 r tan (\frac{θ}{2})$

$2 r cot (\frac{θ}{2})$

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

2rsin(2θ​)

2rcos(2θ​)

2rtan(2θ​)

2rcot(2θ​)

The linear displacement, △​r=r2​​−r1​​; where r2​=r1​=r Hence, ∣Δr∣=r22​+r12​−2r2​r1​cosθ​ <br/>⟹∣Δr∣=2r2−2r2cosθ​<br/> <br/>⟹∣Δr∣=2​r1−cosθ​<br/> <br/>⟹∣Δr∣=2rsin(2θ​)<br/>

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

$2 r sin (\frac{θ}{2})$

$2 r cos (\frac{θ}{2})$

$2 r tan (\frac{θ}{2})$

$2 r cot (\frac{θ}{2})$