1. Tardigrade
  2. Question
  3. Physics
  4. From a given sample of uniform wire, two circular loops P and Q are made, P of radius r and Q of radius n r. If the M.I. of Q about its axis is 4 times that of P about its axis (assuming wire diameter much smaller than either radius of the loops), the value of n is:

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Q. From a given sample of uniform wire, two circular loops $P$ and $Q$ are made, $P$ of radius $r$ and $Q$ of radius $n r$. If the M.I. of $Q$ about its axis is 4 times that of $P$ about its axis (assuming wire diameter much smaller than either radius of the loops), the value of $n$ is:

System of Particles and Rotational Motion

Solution:

$I_{P}=m r^{2}, I_{Q}=(n m)(n r)^{2}=n^{3} m r^{2}$
Now $I_{Q}=4 I_{P} \Rightarrow n^{3} m r^{2}=4 m r^{2} $
$\Rightarrow n=(4)^{1 / 3}$