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

A particle of mass m moves along a circular path of radius r with a centripetal acceleration `a_n` changing with time t as `a_n=kt^2`, where k is a positive constant. The average power developed by all the forces acting on the particle during the first `t_0` seconds is

A

(a) `mkrt_0`

B

(b) `(mkrt_0^2)/(2)`

C

(c) `(mkrt_0)/(2)`

D

(d) `(mkrt_0)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `a_n=kt^2`
or `(v^2)/(r)=kt^2` or `v^2=krt^2`
Therefore, average power delivered `=` Total work done/Total time elapsed
`=`Increase in KE/Total time elapsed
or `ltPgt(1/2m(v^2-0^2))/(t_0)=m/2(krt_0^2)/(t_0)=(mkrt_0^2)/(2)`
Alternative: `v=sqrt(krt)impliesa_1=sqrt(kr)`
`P=F_tv=ma_tv=mkrt`
`ltPgt =(underset0overset(t_0)intPdt)/(t_0)=1/2mkrt_0^2`
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Knowledge Check

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