A composite rod comprising two rods of mass `m` and `2m` and each of length `l = 1 m` as shown in the figure. Assume `omega = 10 rad//s` and `m = 1 kg`, the `KE` of the rotating composite rod is.
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Options

A. 125 J
B. 150 J
C. 250 J
D. 175 J

Answer

C

Explanation

( c) Moment of inertia of composite rod about `P`
`I_p = (ml^2)/(3) + ((2 m)l^2)/(12) + 2m ((3)/(2)l)^2 = 5 ml^2`
Total kinetic energy `k` total `= (1)/(2) I_p omega^2`
=`(1)/(2) (5 m l^2) omega^2 = (5)/(2) ml^2 omega^2 = 250 J`.
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