From a uniform wire, two circular loops are made (i) P of radius r and (ii) Q of radius nr. If the moment of inertia of about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than i or nr)

Options

A. `8sqrt2`
B. `6sqrt2`
C. `4sqrt2`
D. `2sqrt2`

Answer

(d)

Explanation

Moment of inertia of a circular loop, `I=mr^(2)` (Given)
`I=8I_(p)`
`m(r_(Q))^(2)=8[mxxr^(2)_(p)]`
rArr ` (nr)^(2)=8xx(r)^(2)`
implies `n^(2)=8`
`rArr n=sqrt8=2sqrt2`