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A particle is rotates in a circular path...

A particle is rotates in a circular path of radius `54m` with varying speed `v=4t^(2)` . Here `v` is in `m//s` and `t` in second . Find angle between velocity and acceleration at `t=3s` .

A

`theta=30^(@)`

B

`theta=90^(@)`

C

`theta=45^(@)`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
C
`a_(t)=(dv)/(dt)=8t`
`a_(r)=(v^(2))/(R)=((4t^(2))^(2))/(54)=(8)/(27)t^(4)`
At `t=3s` ,
`a_(t)=24m//s^(2)` ltlbrgt `a_(r)=24m//s^(2)`
`tantheta=(a_(t))/(a_(r))=1`
:. `theta=45^(@)`
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