Question

Two circular loops A and B of radii $r_A$ and $r_B$ respectively are made from a uniform wire. If the ratio of their moments of inertia about axes passing through their centres and perpendicular to their planes is $\frac{I_B}{I_A}=8$, then $\left(\frac{r_B}{r_A}\right)=$

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (A)

2

Mass $m$ is directly proportional to length of loop which is $2\pi r$.

$\frac{I_B}{I_A}=8=\frac{m_B{r}_B^2}{m_A{r}_A^2}$

$8=\frac{2\pi r_B^3}{2\pi r_A^3}$

$\frac{r_B}{r_A}=2$