A particle A moves along a circle of radius `R=50cm` so that its radius vector r relative to the point O(figure) rotates with the constant angular velocity `omega=0.40rad//s`. Find the modulus of the velocity of the particle, and the modulus and direction of its total acceleration.

Options

A. `v=0.4 m//s, a=0.4 m//s^(2)`
B. `v=0.32 m//s, a=0.32 m//s^(2)`
C. `v=0.32 m//s, a=0.4 m//s^(2)`
D. `v=0.4 m//s, a=0.32 m//s^(2)`

Answer

D

Explanation

Angular velocity `omega` about centre `=2omega`
`=2xx0.40=0.30 rad//sec`
`v=omega R`
`=0.80xx1/2=0.40 m//s`
`a=v^(2)/R=(0.40xx0.40xx100)/50=0.32 cm//s^(2)`