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A particle is moving uniformly in a circ...

A particle is moving uniformly in a circular path of radius r. When it moves through an angular displacement `theta`, then the magnitude of the corresponding linear displacement will be

A

2 r cos`((theta)/(2))`

B

2 r cot`((theta)/(2))`

C

2 r tan`((theta)/(2))`

D

2 r sin`((theta)/(2))`

Text Solution

Verified by Experts

Here, `angleAOD = (theta)/(2) = angleBOD, AO = r, AD = BD`
From `Delta AOD`
sin`(theta)/(2) = (AD)/(OA)` or, AD = r sin `(theta)/(2)`
`therefore` Linear displacement,
AB = 2`xx` AD = 2 r sin`(theta)/(2)`
The option D is correct.
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