Question

From a solid sphere of mass ‘m' and radius ‘r' a solid cylinder of maximum possible volume is cut. Moment of inertia of the solid cylinder about its axis is:-

Answer 1

Answer:

Correct option is

C

93π4MR2

When the volume of the cube is maximum, the longest diagonal of cube will be equal to diameter of the sphere.

∵FG=GC=L⇒FC=(FG)2+(GC)2=L2+L2=2L⇒FD=(FC)2+(CD)2=(2L)2+L2=3L⇒3L=2R⇒L=32R

Since mass∝volume, we have

MSMC=VSVC⇒MC=VSVC×MS⇒MC=34πR3(32R)3×M⇒MC=3π2M

And moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is given by

I=61ML2⇒I=61×3π2M×(32R)2=93π4MR2