A uniform solid cylinder of length L and radius R has moment of inertia about its axis equal to I_1. A small cocentric cylinder of length L/2 and radius R/3 carved from this cylinder has moment of in…

Question

A uniform solid cylinder of length L and radius R has moment of inertia about its axis equal to I_1. A small cocentric cylinder of length L/2 and radius R/3 carved from this cylinder has moment of inertia about its axis equals to I_2. The ratio I_1/I_2 is \_ \_ \_ \_ .

Accepted Answer

Correct answer: 162. (162) For solid cylinder: I= 12mR^2 Large cylinder: mass m_1= ρπR^2L, so I_1= 12 ρπR^2L R^2= ρπR^4L2 Small cylinder (carved out): length L/2, radius R/3, mass m_2= ρπ (R/3 )^2 (L/2 )= ρπR^2L18 I_2= 12 ρπR^2L18 (R/3 )^2= 12 ρπR^2L18 R^29= ρπR^4L324 I_1I_2= ρπR^4L/2 ρπR^4L/324= 3242=162

$A uniform solid cylinder of length L and radius R has moment of inertia about its axis equal to I_{1} . A small cocentric cylinder of length L /2 and radius R /3 carved from this cylinder has moment of inertia about its axis equals to I_{2} . The ratio I_{1} / I_{2} is____.$

Solution

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