Q192 / 200 · AP EAMCET 2001 · Physics

From a uniform wire, two circular loops are made (i) $P$ of radius $r$ and (ii) $Q$ of radius $n r$. If the moment of inertia of $Q$ 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 $n r$ )

  • A
    $8 \sqrt{2}$
  • B
    $6 \sqrt{2}$
  • C
    $4 \sqrt{2}$
  • Correct answer
    D
    $2 \sqrt{2}$

Solution

Moment of inertia of circular loop, $I=m r^2$ Given, $\begin{aligned} I_Q & =8 I_D \\ m r_Q^3 & =8 m_p r_D^2\end{aligned}$ $\begin{aligned} m_p \times\left(n r_p\right)^2 & =8 m_p \times r_p^2 \\ n^2 & =8 \Rightarrow n=2 \sqrt{2}\end{aligned}$

Hence, the correct answer is option: 'D'.

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