Two circular loops P and Q of radii ' r 'and ' nr ' are made respectively from a uniform wire. Moment of inertia of loop Q about its axis is four times that of loop P about its axis. The value of ' n ' is

Step-by-step solution

The two loops are formed from the same wire. Hence, the linear density will remain constant. = M _ P ~L _ p = M _ Q ~L _ Q array ll & M _ P = L _ P = (2 R _ P )=2 r & Similarly, & M _ Q = L _ Q = (2 R _ Q )=2 ( nr ) & Also, M.I. of circular loop P is, & I _ P = M _ P r ^2=2 r ( r )^2=2 r ^3 & and that of loop Q , & I _ Q = M _ Q ( nr )^2=2 ( nr ) ( nr )^2=2 n ^3 r ^3 & Given ^2 that, I _ Q =4 I _ P & 2 n ^3 r ^3 =4 2 r ^3 n ^3=4 & n =(4)^ 1 3 =(2)^ 2 3 array