During the derivation of centripetal acceleration

PHYSICS · Single correct · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

During the derivation of centripetal acceleration, the change in velocity vector

\Delta\mathbf v

and the change in position vector

\Delta\mathbf r

over a very small time interval satisfy a relation based on the similarity of triangles. Which relation is used? (a)

\dfrac{|\Delta\mathbf v|}{v}=2\,\dfrac{|\Delta\mathbf r|}{r}

(b)

\dfrac{|\Delta\mathbf v|}{v}=\dfrac{|\Delta\mathbf r|}{2r}

(c)

\dfrac{|\Delta\mathbf v|}{v}=\dfrac{|\Delta\mathbf r|}{r}

(d)

\dfrac{|\Delta\mathbf v|}{v}=\left(\dfrac{|\Delta\mathbf r|}{r}\right)^2