From a given sample of uniform wire, two circular loops moment of inertia of O about its axis is 4 times that of P about its axis (assuming wire diameter much smaller, than either radius), the value of n is

Options

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

Answer

B

Explanation

Given `I_(Q) = 4 I_(P)`
Here I = mass `xx "(radius)"^(2)`
If `mu` be the linear mass density (mass/length) of the wire , then `mu xx 2pi (n r) xx n^(2) r^(2) = 4 (mu xx 2pi r xx r^(2))`
On solving , we get `n^(3) = 4` or `n = (4)^(1//3)`