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

Moment of inertia of a loop is,
`I = Mr^(2) = (2pirArho)r^(2)`
Therefore `I prop r^3`
For the two loops.
`r_(2)/r_(1) = (I_(2)/I_(1))^(1/3)`
As `I_(2) = 4I_(1)`
`r_(2)/r_(1) = (4/1)^(1/3)`