Two loops P and Q are made from a uniform wire. The redii of P and Q are `r_(1)and r_(2)` respectively, and their moments of inertia are `I_(1)and I_(2)` respectively, If`I_(2)=4I_(1),"then" r_(2)/r_(1)"equals"`-

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 rxxAxxd`
`I=2pirxxAxxdxxr^(2)=(2piAd)xxr^(3)`
`I prop r^(3)impliesr prop (I)^((1)/3)`
:. `(r_(2))/(r_(1))=((I_(2))/(I_(1)))^((1)/(3))=(4)^((1)/(3))`