Rotation 1 Question 12

15. From a solid sphere of mass M and radius R, a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is

(a) MR2322π

(b) 4MR293π

(c) MR2162π

(d) 4MR233π

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Answer:

Correct Answer: 15. (b)

Solution:

  1. Maximum possible volume of cube will occur when

3a=2Ra=23R

Now, density of sphere, ρ=M43πR3

Mass of cube, m=( volume of cube )(ρ)=(a3)(ρ)

=23R3m43πR3=23πM

Now, moment of inertia of the cube about the said axis is



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