If two circular discs A and B are of same mass but of radii r and 2r respectively, then the moment of inertia of A is

Options

A. the same as that of B
B. twice that of B
C. four times that of B
D. one-fourth that of B

Answer

D

Explanation

Given, radius of circular disc, `A, r_(1)=r`
Radius of circular disc B, `r_(2)=2r`
For disc A, `I_(A)=mr^(2)`…(i)
For disc B, `I_(B)=m(2r)^(2)=4mr^(2)`…(ii)
Dividing Eq. (i) by Eq. (ii), we get
`:. (I_(A))/(I_(B))=(mr^(2))/(4mr^(2))rArr(I_(A))/(I_(B))=(1)/(4)rArr I_(A)=(1)/(4)I_(B)`
So, `I_(A)`= one fourth that of B.