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A disc of radius R rolls on a horizontal...

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

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`

Text Solution

Verified by Experts

The correct Answer is:
A
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))`
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