A disc of radius `R` rolls on a horizontal ground with linear acceleration `a` and angular acceleration `alpha` as shown in Fig. The magnitude of acceleration of point `P` as shown in the figure at an instant when its linear velocity is `v` and angular velocity is `omega` will be a

Options

A. `sqrt((a + r prop)^2 + (r omega^2)^2)`
B. `(ar)/( R)`
C. `sqrt(r^2 prop^2 + r^2 omega^4)`
D. `r prop`

Answer

A

Explanation

(a) `vec a_o = a hat i, vec a_(p//o) = prop r hat i + omega^2 r(- hat j)`
`vec a_p = vec a_o + vec a_(p//o) =(a + prop r) hat i - omega^2 r hat j`
`a_p = sqrt((a + prop r)^2 + (omega^2 r)^2)`.