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The angular displacement of the rod is d...

The angular displacement of the rod is defied a s`0=(3)/(20) t^(2)` where `theta` is in radian and t is in second. The collar B slides along the rod in such a way that its distance from O is `r=0.9-0.12t^(2)` where r is in metre and t is secnd The velocity of collar at `theta=30^(@)` is

A

`0.45 m//s`

B

`0.48 m//s`

C

`0.52 m//s`

D

`0.27 m//s`

Text Solution

Verified by Experts

(c) `:.v_(r)=(Dr)/(dt)=-024t`
`v_(1)romega=r("d"theta)/(dt)=r((6)/(20)t)=(0.9-0.12t^(2))((6t)/(20))`
`:." "v=(sqrt(v_(r)^(2)+v_(t^(2)))`
`:.theta=(3)/(20)t^(2)or(pi)/(6)=(3)/(20)t^(2)`
`:." " t=sqrt(((20pi)/(18)))`
Putting the value of `theta, v=0.25m//s`
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