In the given figure, `a=15m//s^(2)` represents the total acceleration of a particle moving in the clockwise dirction in a circle of radius `R=2.5`m at a given instant of time. The speed of the particle is

Options

A. `4.5`m/w
B. `5.0` m/s
C. `5.7` m/s
D. `6.2`m/s

Answer

C

Explanation

Centripetal acceleration of a particle moving on a circular path is given by
`a_(C)=(V^(2))/(R)`
In the given figure,
`a_(C)=a cos 30^(@)=15 cos 30^(@)ms^(-2)`
`rArr" "(v^(2))/(R)=15 cos 30^(@)`
`rArr" "v^(2)=Rxx15xx(sqrt3)/(2)=2.5xx13xx(sqrt3)/(2)`
`therefore" "v=5.7ms^(-1)`