Choose the correct option:
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 + ralpha)^(2) + (r omega^(2))^(2))`
B. `(ar)/R`
C. `sqrt(r^(2)alpha^(2) + r^(2) omega^(4))`
D. `r alpha`

Answer

A

Explanation

Linear velocity of p is `v + r omega rArr` Linear acceleration `=d/(dt) (v+ romega) = a + romega`
Angular velocity `=omega rArr` radial acceleration `=omega^(2)r`
`rArr` total acceleration of `p propto sqrt((a+r alpha)^(2)+(omega^(2)r^(2))`