A car moves around a curve at a constant speed. When the car goes around the arc subtending `60^(@)` at the centre, then the ratio of magnitude of instantaneous acceleration to average acceleration over the `60^(@)` arc is `:`

Options

A. `(pi)/(3)`
B. `(pi)/(6)`
C. `(2pi)/(3)`
D. `(5pi)/(3)`

Answer

A

Explanation

`|Delta V| = sqrt(v^(2)+v^(2)-2v^(2) cos 60^(@))`
`= va_(av) = (|Delta vec(v)|)/(Delta t)=(v)/(t) =(3v^(2))/(pi R)`
`rArr a=(v^(2))/(R") , (a_(i))/(a_(av)) = (v^(2) pi R)/(R xx 3v^(2)) = (pi)/(3)`