From a given sample of uniform wire, two circular loops `P` and `Q` are made, `P` of radius `r` and `Q` of radius `nr`. If the M.I. of `Q` about its axis is four times that of `P` about its axis (assuming the wire to be of 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

(b) `I_p = mr^2, I_Q = (nm)(nr)^2 = n^3 mr^2`
Now `I_Q = 4 I_P rArr n^3 mr^2 = 4 mr^2 rArr n = (4)^(1//3)`.