A, B and C are disc, solid sphere and spherical shell respectively...

\mathrm{A}, \mathrm{B}

and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure.
A, B and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed

A, B and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed

The moment of inertia of the given system about

P Q

\frac{X}{15} I

, where

I

is the moment of inertia of the disc about its diameter. The value of x is _______.

Correct answer

Step-by-step solution

All bodies have same mass and same radius.

\mathrm{A} \rightarrow

Disc

\mathrm{B} \rightarrow

Solid sphere

\mathrm{C} \rightarrow

Spherical shell
and,

\mathrm{I}=\frac{\mathrm{MR}^2}{4}

\mathrm{I}_{\mathrm{PQ}}=\frac{\mathrm{MR}^2}{4}+\left(\frac{2}{5} \mathrm{MR}^2+\mathrm{MR}^2\right)+\left(\frac{2}{3} \mathrm{MR}^2+\mathrm{MR}^2\right)

\mathrm{I}_{\mathrm{PQ}}=\frac{15 \mathrm{MR}^2+24 \mathrm{MR}^2+60 \mathrm{MR}^2+40 \mathrm{MR}^2+60 \mathrm{MR}^2}{60}

\mathrm{I}_{\mathrm{PQ}}=\frac{199}{60} \mathrm{MR}^2=\frac{199}{15}\left(\frac{\mathrm{MR}^2}{4}\right)

=\frac{199}{15} \mathrm{I}

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