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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 I_1 be the moment of inertia of the disc about its axis and I_2 be the moment of inertia of the new sphere about its axis. The ratio I_1/I_2 is given by :

140

185

65

285

Solution:

Correct option is D. 140
Disc : I_disc = (7M/8) × (2R)²/2 = I_1
Solid sphere : M/8 = (4/3πr³ρ
ρ(4/3πr³)/8 = ρ
(4/3πr³)R² = r = radius of the solid sphere
I_ss = (m/8r² ) × (2/5) = M/8 × (R²/2)² × (2/5) = I_2
so that, I_1/I_2 = (7M/8) × (2R²/2) / (2/5) × (M/8) × (R²/2) = 140