A uniform sphere of mass m, radius r and moment of inertia I about its centre moves along the x-axis as shown in figure. Its centre of mass moves with velocity = v0, and it rotates about its centre of mass with angular velocity = ω0. Let L→=Iω0+mv0r(−k~). The angular momentum of the body about the origin O is

L→=R→×mv→0+Iω→0=mv0+Iω0 (which is constant)

L→=R→×mv→0+Iω→0=mv0+Iω0 (which is constant)

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A uniform sphere of mass m, radius r and moment of inertia I about its centre moves along the x-axis as shown in figure. Its centre of mass moves with velocity = v₀, and it rotates about its centre of mass with angular velocity = $ω_{0}$ . Let $\vec{L} = ({Iω}_{0} + {mv}_{0} r) (- \tilde{k})$ . The angular momentum of the body about the origin O is

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$\vec{L}, only if v_{0} = ω_{0} r$

greater than $\vec{L}, if v_{0} > ω_{0} r$

less than $\vec{L}, if v_{0} > ω_{0} r$

$\vec{L}$ , for all values of $ω_{0} and v_{0}$

answer is D.

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$\vec{L} = \vec{R} \times m {\vec{v}}_{0} + I {\vec{ω}}_{0} = {mv}_{0} + {Iω}_{0}$ (which is constant)

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