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

Answer

C

Explanation

As `I=Mr^(2)` and length of circular loop `=2pir`
`:.` Mass of Q =nM
Given `I_(Q)=4I_(P)`
nM(nr)^(2)=4M(r)^(2)`
`n^(3)=4`
`n=(1)/(4^(3))`