Two circular loops A and B are made of the same wire and their radii are in the ratio 1:n. Their moments of inertia about the axis passing, through the center and perpendicular to their planes are in the ratio 1:m.The relation between m and n is

Question

Two circular loops A and B are made of the same wire and their radii are in the ratio 1:n. Their moments of inertia about the axis passing, through the center and perpendicular to their planes are in the ratio 1:m.The relation between m and n is (A) m=n (B) m=n2 (C) m=n3 (D) m=n4

Tardigrade Admin · Accepted Answer

(I1/I2) = (M1R21/M2R22) for a circular loop, M α R ∴ (I1/I2) = (R31/R32)

Q. Two circular loops A and B are made of the same wire and their radii are in the ratio 1:n. Their moments of inertia about the axis passing, through the center and perpendicular to their planes are in the ratio 1:m.The relation between m and n is

m=n

$m = n^{2}$

$m = n^{3}$

$m = n^{4}$

$\frac{I _{1}}{I _{2}} = \frac{M _{1} R _{1}^{2}}{M _{2} R _{2}^{2}}$ for a circular loop, $M α R$
$∴$ $\frac{I _{1}}{I _{2}} = \frac{R _{1}^{3}}{R _{2}^{3}}$

Q. Two circular loops A and B are made of the same wire and their radii are in the ratio 1:n. Their moments of inertia about the axis passing, through the center and perpendicular to their planes are in the ratio 1:m.The relation between m and n is

m=n

m=n2

m=n3

m=n4

I2​I1​​=M2​R22​M1​R12​​ for a circular loop, MαR ∴ I2​I1​​=R23​R13​​

$m = n^{2}$

$m = n^{3}$

$m = n^{4}$

$\frac{I _{1}}{I _{2}} = \frac{M _{1} R _{1}^{2}}{M _{2} R _{2}^{2}}$ for a circular loop, $M α R$
$∴$ $\frac{I _{1}}{I _{2}} = \frac{R _{1}^{3}}{R _{2}^{3}}$