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A particle travels along the arc of a ci...

A particle travels along the arc of a circle of radius `r`. Its speed depends on the distance travelled `l` as `v=asqrtl` where 'a' is a constant. The angle `alpha` between the vectors of net acceleration and the velocity of the particle is

A

`alpha=tan^(-1)(2l//r)`

B

`alpha=cos^(-1)(2l//r)`

C

`alpha=sin^(-1)(2l//r)`

D

`alpha=cot^(-1)(2l//r)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let, when particle is at angular position `alpha`, then distance travelled = `l`
`v=asqrtl`, But`a_(t)=(dv)/(dt)=a/(2sqrtl)(dl)/(dt)=(av)/(asqrtl)=a^(2)/2`
and `a_(c)=v^(2)/r=((a^(2)l)/r)`
Angle between `a_("net")` & `a_(t):, alpha=tan^(-1)((2l)/r)`
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