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 4 times than that of P, then value of n is :

Options

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

Answer

A

Explanation

Here `I_(Q)=4I_(P)`. Let m be the mass per unit length of wire.
`therefore mxx2pinr(nr)^(2)=4[(m2pir)r^(2)]`
implies `n^(3)=4impliesn=4^(1//3)`