Two circular loops P and Q of radii r and nr | vedclass

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(A) Let $\lambda$ be the mass per unit length of the wire.The mass of loop $P$ is $M_P = \lambda (2 \pi r)$ and its radius is $r$.The moment of inerti

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$(2)^{2/3}$

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(A) Let $\lambda$ be the mass per unit length of the wire.The mass of loop $P$ is $M_P = \lambda (2 \pi r)$ and its radius is $r$.The moment of inertia of loop $P$ about its axis is $I_P = M_P r^2 = \lambda (2 \pi r) r^2 = 2 \pi \lambda r^3$.The mass of loop $Q$ is $M_Q = \lambda (2 \pi nr)$ and its radius is $nr$.The moment of inertia of loop $Q$ about its axis is $I_Q = M_Q (nr)^2 = \lambda (2 \pi nr) (nr)^2 = 2 \pi \lambda n^3 r^3$.Given that $I_Q = 4 I_P$,we have $2 \pi \lambda n^3 r^3 = 4 (2 \pi \lambda r^3)$.Simplifying this,we get $n^3 = 4$.Therefore,$n = 4^{1/3} = (2^2)^{1/3} = 2^{2/3}$.

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

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