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  • Two spherical shells of mass '1kg' each and radius '1m' are connected with a massless rod of length '2m'. Then the moment of inertia of the system about an axis passing thro

Two spherical shells of mass '1kg' each and radius '1m' are connected with a massless rod of length '2m'. Then the moment of inertia of the system about an axis passing through the centre of one of the shells and perpendicular to the rod.

Option: 1

\frac{4}{3} \mathrm{~kg}\mathrm{m}^2


Option: 2

4 \mathrm{~kg}\mathrm{m}^2


Option: 3

\frac{8}{3} \mathrm{~kg}\mathrm{m}^2


Option: 4

\frac{16}{3} \mathrm{~kg}\mathrm{m}^2


Answers (1)

best_answer

Assuming, mass of each spherical shell is 'm' and radius 'r' then

I_{\text {Total }}=\frac{2}{3} m r^2+\left(\frac{2}{3} m r^2+m(2 r)^2\right)

=\frac{4}{3} m r^2+4 m r^2=4 m r^2 \times \frac{4}{3}

=\frac{16}{3} m r^2 =\frac{16}{3} \times 1 \times 1^2 =\frac{16}{3} \mathrm{~kg}\mathrm{m}^2

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Rishi

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