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:

4MR²

____

9√3π

Explanation:

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

=

L

2

+L

2

=

2

L

⇒FD=

(FC)

2

+(CD)

2

=

(

2

L)

2

+L

2

=

3

L

⇒

3

L=2R

⇒L=

3

2R

Since mass∝volume, we have

M

S

M

C

=

V

S

V

C

⇒M

C

=

V

S

V

C

×M

S

⇒M

C

=

3

4

πR

3

(

3

2R

)

3

×M

⇒M

C

=

3

π

2M

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

I=

6

1

ML

2

⇒I=

6

1

×

3

π

2M

×(

3

2R

)

2

=

9

3

π

4MR

2