A , B and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure. The moment of inertia of the given system about PQ is 15 X

Question

A , B and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure. The moment of inertia of the given system about PQ is 15 X ​ I , where I is the moment of inertia of the disc about its diameter. The value of x is _______.

TestHub · Accepted Answer

All bodies have same mass and same radius.
$A \to$ Disc
$B \to$ Solid sphere
$C \to$ Spherical shell
and, $I = \frac{MR ^{2}}{4}$
$I_{PQ} = \frac{MR ^{2}}{4} + (\frac{2}{5} MR^{2} + MR^{2}) + (\frac{2}{3} MR^{2} + MR^{2})$
$I_{PQ} = \frac{15 MR ^{2} + 24 MR ^{2} + 60 MR ^{2} + 40 MR ^{2} + 60 MR ^{2}}{60}$
$I_{PQ} = \frac{199}{60} MR^{2} = \frac{199}{15} (\frac{MR ^{2}}{4})$
$= \frac{199}{15} I$

Physics - Rotation Question with Solution | TestHub

Doubts & Discussion