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

Answer

A

Explanation

Here if `M_(P)andM_(Q)` are the masses of two rings, then
`(M_(P))/(M_(Q))=(2piR_(P))/(2pinR_(p))=(1)/(n)`
`therefore M_(P)//M_(Q)=(1)/(n)`
`M_(P)=(M_(Q))/(n)" "...(i)`
Also we are given that
`I_(Q)=4I_(p)` Putting the values
`m_(Q).n^(2)R_(P)^(2)=4m_(P)R_(P)^(2)`
`m_(Q)n^(2)=4(1)/(n)xxm_(Q)`
or `n^(3)=4orn=4^(1//3)`