X and Y are two loops made from same wire. The radii of X and Y are `r_(1)` and `r_(2)` and their M.I are `I_(1)` and `I_(2)` . If `I_(2)//I_(1)=4` the value of `r_(2)/r_(1)` is `(K)^(1//3)`. Find the value of K.

Options

A. `4^(2//3)`
B. `4^(1//3)`
C. `4^(-2//3)`
D. `4^(-1//3)`

Answer

B

Explanation

`I= Mr^(2)`
M  (Volume `xx` density) = `AL xx d`
`M= 2pi r xx A xx d`
`I= 2pi r xx A xx d xx r^(2)= (2pi Ad) xx r^(3)`
`I prop r^(3) rArr prop (I)^((1)/(3))`
`therefore (r_(2))/(r_(1))= ((I_(2))/(I_(1)))^((1)/(3))= (4)^((1)/(3))`