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

Answer

B

Explanation

`I_(1)=m_(1)r_(1)^(2)` and `I_(2)= m_(2)r_(2)^(2)`
`rho = (m_(1))/(l_(1)) therefore m_(1)= rho l_(1)` and `m_(2)=rho l_(2)`
`(m_(1))/(m_(2))=(l_(1))/(l_(2))=(2pi r_(1))/(2pi r_(2))`
`therefore (I_(1))/(I_(2))=(r_(1)^(2))/(r_(2)^(2))xx(r_(1))/(r_(2)) therefore (r_(1))/(r_(2))= root(3)(4)`