Question

Two rings having same moment of inertia have their radii in the ratio $1:4$. Their masses will be in the ratio

• A. $4:1$
• B. $16:1$
• C. $1:4$
• D. $2:1$

Answer 1

Answer: (B)

$16:1$

$I_1=I_2$ (Same moment of Inertia)

$M_1{R}_1^2=M_2{R}_2^2$

$\frac{R_1}{R_2}=\frac{1}{4}\Rightarrow 4R_1=R_2$

$M_1{R}_1^2=M_2(4R_1{)}^2$

$M_1{R}_1^2=16M_2{R}_1^2$

$\frac{M_1}{M_2}=\frac{16}{1}=16:1$