Show that moment of inertia of a solid body of any shape change eith temperature as I=I_0(1+2 alhatheta). Where I_0 is the moment of inertia at 0^C nad alpha is the coefficient of liear expansion of the solid.

Show that moment of inertia of a solid body of any shape change eith t

1.	Show that moment of inertia of a solid body of any shape change eith temperature as I=I_0(1+2 alhatheta). Where I_0 is the moment of inertia at 0^C nad alpha is the coefficient of liear expansion of the solid.
Answer» SOLUTION :Given, `I_0= moment of inertia at 0^@C` ` alpha= Coefficient of inertia ` expansion ` To prove I=I_0 (1+2 alpha theta) Let the temperature changes to `theta` from `0^@C` `Delta T= theta` ` Let R_0 be the radius of gyration ` ` Now R_0=R(1+ alpha theta)` `I_0=MR^2 where M is the MASS. ` ` Now I=MR^2=MR^2 ((1+alpha theta)^2)` ` [by binominal expansion and neglecting alpha_2 theta_2 which is a very SMALL VALUE]` `=MR^2(1+2 alpha theta)` ` So,I=I_0(1+2 alpha theta).........(proved).`