Two rings of radius R and n R made of same material have the ratio of moment of inertia about an axis passing through centre in 1: 8. The value of n is

Question

Two rings of radius R and n R made of same material have the ratio of moment of inertia about an axis passing through centre in 1: 8. The value of n is (A) 2 (B)  bar2 (C) 4 (D) (1/2)

Tardigrade Admin · Accepted Answer

Ratio of moment of inertia of the rings

\frac{I _{1}}{I _{2}} = (\frac{M _{1}}{M _{2}}) (\frac{R _{1}}{R _{2}})^{2} = (\frac{λ L _{1}}{λ L _{2}})^{2} (\frac{R _{1}}{R _{2}})^{2}

= (\frac{2 π R}{2 πn R}) (\frac{R}{n R})^{2}

[λ =

linear density of wire

=

constant ]

\Rightarrow \frac{L _{1}}{L _{2}} + \frac{1}{n _{3}} + \frac{1}{8}

(given)

∴ n^{3} = 8

\Rightarrow n = 2

Q. Two rings of radius $R$ and $n R$ made of same material have the ratio of moment of inertia about an axis passing through centre in $1 : 8$ . The value of $n$ is

$2$

$\overset{ˉ}{2}$

$4$

$\frac{1}{2}$

Q. Two rings of radius R and nR made of same material have the ratio of moment of inertia about an axis passing through centre in 1:8. The value of n is

2

2ˉ

4

21​

Ratio of moment of inertia of the rings I2​I1​​=(M2​M1​​)(R2​R1​​)2=(λL2​λL1​​)2(R2​R1​​)2 =(2πnR2πR​)(nRR​)2 [λ= linear density of wire = constant ] ⇒L2​L1​​+n3​1​+81​ (given) ∴n3=8 ⇒n=2

Q. Two rings of radius $R$ and $n R$ made of same material have the ratio of moment of inertia about an axis passing through centre in $1 : 8$ . The value of $n$ is

$2$

$\overset{ˉ}{2}$

$4$

$\frac{1}{2}$