Two point masses each of mass m are attached to ends of a massless rod of length $2 l .$ z–axis passes through mid point O of rod and vertical. Rod is fixed at point O and rotates about z–axis with constant angular velocity $ω .$ Which of the following statement(s) is/are INCORRECT? (Angular momentum of system about O is $\vec{L}$ )

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Torque on system is zero

Angular momentum of system $(\vec{L})$ and its angular velocity $\vec{ω}$ are parallel as $\vec{L} = I \vec{ω}$

Angular momentum of system is $2 m ω l^{2} \cos^{2} θ$

Angular momentum of system $(\vec{L})$ is related to torque acting on system as $\vec{τ} = \frac{d \vec{L}}{d t}$ about any point (on the system or off the system)

answer is A, B, C.

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Detailed Solution

Angular momentum of system about O is L.
Question Image
$| L | = 2 m l^{2} \cos θ^{/}$
$L_{z} = L \cos θ^{/} = 2 m ω l^{2} \cos^{2} θ^{/}$
$L_{z} = 2 m ω l^{2} \sin^{2} θ = m v l \cos θ^{/}$