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NEET 2015 (AIPMT, Cancelled Paper) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from NEET 2015 (AIPMT, Cancelled Paper)

Q178NEET 2015 · AIPMT · CANCELLED PAPERMedium

Moment of Inertia & Radius of Gyration

Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX' axis is

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Answer: (b)

Shell on the axis (diameter): $\frac{2}{3}mr^2$ .
Two shells touching the axis ( $d = r$ ): $2\left(\frac{2}{3}+1\right)mr^2 = \frac{10}{3}mr^2$ .
$I = \frac{12}{3}mr^2 = 4mr^2$ , so the answer is (b).

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