A solid sphere of mass 50 kg and radius 20 cm is rotating about its diameter with an angular velocity of 420…

A solid sphere of mass 50 kg and radius 20 cm is rotating about its diameter with an angular velocity of 420 rpm . The angular momentum of the sphere is
  1. 8.8 Js
  2. 70.4 Js
  3. 17.6 Js
  4. 35.2 Js

Solution

$\mathrm{m}=50 \mathrm{~kg}, \mathrm{v}=20 \mathrm{~cm}=0.2 \mathrm{~m}$ $\omega=420 \mathrm{rpm}=\frac{2 \pi \times 420}{60} \mathrm{rad} / \mathrm{s}=14 \pi \mathrm{rad} / \mathrm{s}$ The angular momentum of solid sphere, $\mathrm{L}=\mathrm{I} . \omega=\frac{1}{5} \mathrm{mr}^2 \omega=\frac{2}{5} \times 50 \times 0.2 \times 0.2 \times 14 \pi=35.2 \mathrm{Js}$

Asked in: AP EAMCET 2024 (21 May Shift 1)

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