Question

A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of 7M/8
and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let I₁ be the moment of inertia of the disc about its axis and I₂ be the moment of inertia of the new sphere about its axis. The ratio of I₁/I₂ is given by:
(A) 285 (B) 185
(C) 65 (D) 140

Answer 1

Disc :

Idisc=7M8×(2R)22=I1Idisc=7M8×(2R)22=I1

Solid sphere :

M8=(43πr3)ρM8=(43πr3)ρ

ρ(43πr3)8=ρ43πr3ρ(43πr3)8=ρ43πr3

R2=r=radius of the solid sphereR2=r=radius of the solid sphere

Iss=(m8r2)×25Iss=(m8r2)×25

      =M8×(R2)2×25=I2=M8×(R2)2×25=I2

so that, 

I1I2=7M8×(2R2)225×M8×(R2)2=140