Rotational Motion Question 125
Question: A thin wire of length $L$ and uniform linear mass density $\rho $ is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about an axis XY is
Options:
A) $\frac{\rho L^{3}}{8{{\pi }^{2}}}$
B) $\frac{\rho L^{3}}{16{{\pi }^{2}}}$
C) $\frac{5\rho L^{3}}{8{{\pi }^{2}}}$
D) $\frac{3\rho L^{3}}{8{{\pi }^{2}}}$
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Answer:
Correct Answer: D
Solution:
[d] $L=2\pi r\Rightarrow r=\frac{L}{2\pi },m=\rho L$
$l _{xy}=\frac{3}{2}mr^{2}$
$=\frac{3}{2}\rho L{{\left( \frac{L}{2\pi } \right)}^{2}}=\frac{3}{8}\frac{\rho L^{3}}{{{\pi }^{2}}}$
