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A particle of mass m moves along a circl...

A particle of mass `m` moves along a circle of radius `R` with a normal acceleration varying with time as `a_(n) = bt^(2)`, where `b` is a constant. Find the time dependence of the power developed by all the forces acting on the particle, and the mean value of this power averaged over the first `2` seconds after the beginning of motion, `(m = 1,v = 2,r = 1)`.

Text Solution

Verified by Experts

The correct Answer is:
`2`
`rArr v = sqrt(bR) t (dv)/(dt) = sqrt(bR)`
For circular motion work done by normal force is zero. For tangential forces.
`F_(t)=m(dv)/(dt)=m sqrt(bR) P=F_(t).v = F_(t) v cos theta`
as `theta = 0^@`, `P = F_(t) v = mbRt`
Average power `= (underset(0) overset(T) intP(t)dt)/(underset(0) overset(T)int dt) = underset(0) overset(T) int(mbRTdt)/(T)`
=`(mbR(t^(2)//2)_(0)^(T))/(T) = (mbRt)/(2)`.
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