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 equal to __________ .

Options

A. 65
B. 185
C. 285
D. 140

Answer

D

Explanation

`I_("Disc")=(7m)/(8)((2R)^(2))/(2)=I_(1)`
For solid sphere
`(m)/(8)=((4)/(3)pir^(3))rhoimplies(rho((4)/(3)piR^(3)))/(8)=(4)/(3)pir^(3)rho`
`(R)/(2)=r=` Radius of solid sphere
`I_(SS)=((M)/(8)r^(2))(2)/(5)implies(M)/(8)((R)/(2))^(2)(2)/(5)=I_(2)`
So that `(I_(1))/(I_(2))=((7M)/(8)((2R)^(2))/(2))/((2)/(5)(M)/(8)((R)/(2))^(2))=140`